Category 1: Fish Bowls
Myth: Bowls make good homes for fish such as goldfish, bettas, and gouramis.
Status: False
Reasons: Goldfish grow to over a foot and live for decades, but not in a bowl.  Goldfish, therefore, need a tank much larger than a bowl.  The proper home for a goldfish is 20 gallons for one fish, and 10 additional gallons for each additional goldfish.  They should not be kept with fish other than goldfish or Koi.
    Bettas do not belong in bowls for a different reason.  They stay small enough and only live for about 4 years.  But they need water that stays at a constant 78-82° F.  It is very hard to keep a fish bowl at that temperature constantly.  Gouramis, other than dwarf gouramis, grow too big to fit in a gallon bowl.  Some people suggest placing a Paradise Gourami in a bowl.  While the original Paradise fish might have been a strong fish that could live in a bowl, it is still not suggested for today's version (unless it has a close relative that was wild caught).
    A major problem with bowls for any fish is keeping them clean.  The only way to keep a bowl clean is to replace all of the water and wipe it out twice a week.  This causes several problems.  First, it is stressful for the fish to be moved around so much.  Second, if you forget to clean the bowl, there is no bacteria to stop ammonia from building up.
    And one last argument against using bowls is the baby in a closet.  You can keep a baby in a closet for its entire life.  It doesn't have to have much light to survive.  You can change a newspaper for it every day and give it food.  The baby might even survive for a near-normal human life span.  Studies on children who have been treated in this way show that they never get mentally above 4 to 10 years old because they have no one to talk to and they don't learn to socialize properly.  I suspect a fish stuck in 1 gallon of water (or less) by itself would have the same problem.

Category 2: Bettas
Myth: Bettas can be kept in vases with a peace lilly.
Status: True and False
Reasons: If the vase is large enough that a small heater can be placed in it, then yes, the fish can be kept quite easily in a vase with a plant.  But it would have the other problems that regular fish bowls have with cleaning.  Parts of this and connected myths were fabricated by some company selling "betta vases".  It also came with other myths described below.

Myth: Bettas in vases with peace lilies do not need to be fed more than once a week, or not at all.  The reason is that they pick on the roots of the lilies to get food.
Status: False
Reasons: This is a cause of betta death.  Bettas are carnivores.  I have heard arguments against calling them carnivores, but none of them addressed the fact that in the wild bettas only eat meat!  The only argument against calling them carnivores is that it makes them sound like sharks.  Bettas are carnivorous, and deciding on calling them carnivores or omnivores should not be based on how some ignorant people may react but on scientific data.  They eat small ants, mosquito larvae, and other small insects and larvae that get into their water.  They don't eat roots unless they are starving.

Myth: Bettas do not need water changes because they can breath air.  Bettas do not need water changes because of the peace lilly.
Status: False
Reasons: Bettas have gills just like any other fish.  Just because they can breath air doesn't mean their gills don't function.  They do, in fact, burn in the presence of deadly ammonia.  They should be treated just like any other fish.  All fish should be treated with great care, good  filters, steady water conditions, and proper heating.  There is no excuse for not taking proper care of fish.  Even the best peace lilly can't make up for proper maintenance.

Myth: Bettas come from shallow water, ditches, rice fields, and mud puddles.
Status: True
Reasons: Bettas do come from rice fields and can be found in shallow water.  However, it should be remembered that shallow water usually refers to water less than a few feet deep, and rice fields are usually flooded with over a foot of water.  They also live in swamps.  If they live in mud puddles, it is likely that they are only there because they could not escape before the water was drained during the dry season and will be very happy when the land is flooded again.  Just because they come from areas with low oxygen levels, does not mean they come from areas with high ammonia and nitrogen levels.  However, because of where they live, they have been created with an organ to allow them to breath air.  Without that organ they would die.  Other fish that have these organs are gouramis.

Myth: Betta breeders use only a few inches of water for their fish.
Status: True
Reasons: Young Betta splendens are kept in less than 5 inches of water because it is easier for them to get to the surface for air.  It is very important for them to get the surface because they will die without air.  Bettas are sometimes kept in small jars while young due to a lack of space and tanks for them.  Most of the time, each jar is cleaned every day or every other day, and this is only done for the first few months until they are sold to stores.  Other breeders keep their bettas together in a cycled tank to give them room to grow in.

Myth: All bettas are highly aggressive and cannot be kept together.
Status: False
Reasons: Males of the species B. splendens can't be kept together except in a few rare situations where they are raised together.  Females of this species can, however, be kept together.  There are also other species in the Betta genus that may or may not be able to be kept together.

Myth: In Asia, betta fighting is a popular gambling event.
Status: True
Reasons: Sadly, idiots who like to watch suffering purposely place two male bettas together for the fun of watching them fight.  They also gamble on who will win (die last).  In the wild, most information says that the males stay away from each other as much as possible.  It is similar to rooster fighting in America.
[I am not animal rights supporter; I disagree with the law enforcement officers who waste public money taking animals from their owners, and the idea of banning hunting, but if someone purposely harms an animal for the fun of watching it suffer, they sometimes go on to become murderers of humans.]

Category 3: Nitrogen Cycle and Water Conditions
Myth: The cycle takes only a few days.
Status: True and False
Reasons: The cycle under normal conditions takes four to six weeks.  This myth can only be true under a few circumstances.  First, the tank may be seeded with gravel from a cycled tank.  Second, the tank may be seeded with a used filter/bio-wheel from a cycled tank.  Third, there are two products on the market that can cycle a tank over night or in days.

Myth: Products exist with living bacteria that can cycle a tank in days.
Status: True
Reasons: They are Bio Spira from Marineland and Fritz*.  These products have been found to work.  Other products that are not kept refrigerated have not been found to be effective.  If the cycle product is not refrigerated, it most likely will not work as well as those that are kept cold.
* Note that I do not advertise for this product.  However, these products do exist and I felt it would be a good idea to mention them by name.  I have decided to hold the use of the names of similar products that are not as effective and unrefrigerated.  It is my goal to inform you to make good choices without speaking badly of other products that are not as effective.

Myth: A tank can be cycled by setting it up with all new equipment and left for 4 to 6 weeks.
Status: False
Reasons: I have been told that this is possible, but do not personally believe it to be true.  For this to be true, the source water would have to have large amounts of ammonia and bacteria present.  This would most likely be unsafe to drink.  To cycle a tank, there must be ammonia present.

Myth: A tank can be cycled by setting it up with all new equipment or with a used filter or gravel and left for 4 to 6 weeks with the addition of organic and or nitrogenous materials.
Status: True
Reasons: This process is called fish-less cycling, and is considered the best way to cycle a tank by many aquarists.  This process involves placing bottled ammonia, old fish food, or live plants in the tank.  Fish food and live plants will bring in organic compounds that break down and make ammonia.  The plants will also bring in bacteria to begin processing that ammonia.

Myth: Water changes can be done once a month or every few months.  There are products made that claim to be able to stabilize a tank so that water changes are only needed every 6 months.
Status: True and False
Reasons: True experts are the only people this is true for, and even half of them say it should not be done.  For the average aquarist, this myth is false.  Further information withheld to prevent trying it. 

Myth: There are products made that claim to be able to stabilize a tank so that water changes are only needed every 6 months.
Status: True
Reasons: The second part of this myth is true.  Products do exist that claim to be able to extend the time between water changes.  There is no substitute for proper tank maintenance.  Just because they exist doesn't mean they work.  Many aquarium products seem to operate under the old "buyer beware" system and make false or exaggerated claims.

Myth: Live plants are needed for a truly natural and healthy tank.
Status: True
Reasons: Plants are a vital part of the nitrogen cycle in the natural habitat of all aquarium fish.  A tank without them can be healthy, but not natural.  This does not mean hard-to-grow plants must be in your tank.  There are many easy plants, including hornwort, banana plants, java fern, java moss, amazon swords, and some apponogetons.

Myth: Larger tanks are easier to maintain.
Status: True
Reasons: In a larger tank, buildup of dangerous chemicals, including ammonia, nitrite, nitrate, and heavy metals, takes much longer than in smaller tanks.  It may seem like it would be harder to do 25% water changes because there would be more water to remove and replace, but it is better over time.

Category 4: Algae Eaters
Myth: All tanks need algae eaters.
Status: False
Reasons: Proper maintenance and planting will prevent all algae from growing in the tank  You may, however, decide to keep an algae eater just because you like a certain fish.

Myth: Algae eaters can live on nothing but algae, mulm, waste, and left over food on the bottom of the tank.
Status: False
Reasons: Algae eaters often starve due to lack of alternative food.  Many algae eaters do not prefer algae.  They should be fed fresh or frozen squash, algae chips, shrimp pellets, and other vegetables.  They also often need a source of wood in their diets.

Myth: Chinese Algae Eaters make good algae eaters for community tanks.
Status: False
Reasons: CAEs are highly aggressive fish eaters that grow to a foot long at worst, and semi-aggressive fish eaters that grow to 10 inches at best.  They are neither Chinese nor algae eaters.  They eat algae when they are young, but begin eating other things as they grow.  They should not be kept with slow-moving, large, or tall fish because they make easy targets.  Ottos are a better choice.  They stay under 3 inches, and do well in groups.

Category 5: Mythic Generalities
Myth: Fish grow to the size of the tank they are in.  Fish cannot outgrow their tank.
Status: False
Reasons: It is just a plain ridiculous idea.  Fish will grow until they can't fit in their tank if the tank is too small.  A goldfish can grow to half a foot in a 10 gallon tank if water changes are done often enough.  When choosing a fish tank for a certain fish, the tank should be 10 inches long for each inch that the fish MAY reach in the wild.  For example, a neon tetra only grows to 1.5 inches, so should be placed in a tank that is at least 15 inches long.  A clown loach may grow to 10 inches in the wild, so it should be placed in a tank that is 100 inches long.
    The reason this myth came about may be because of people who keep goldfish in 10 gallon tanks.  Staying in such a small area can lead to stunting, causing the fish to max out at a length of about 5-6 inches.  This is a sign of terrible conditions and should not be thought of as normal.  It could also be because goldfish die in such conditions much sooner than they would in an appropriate tank.

Myth: Nemo can live in a 5 gallon tank.  Nemo can live with my other tropical fish.
Status: False
Reasons: Nemo is a saltwater marine fish.  Specifically a clown fish.  This type of fish usually lives in an anemone.  It needs a very stable tank and should not be the first fish ever kept.  Because clown-fish are saltwater fish, they cannot be kept with freshwater fish.  It may be possible to adapt a molly to live in full marine water, but that would require a lot more work than most people would want to do.  Saltwater tanks are not just water with a lot of salt, so you should do a lot of practice with the tank before you ever put a fish into it.

Myth: Swordtail females can become male in the absence of other male swordtails.
Status: False, probably
Reasons: It is most likely that this myth developed for two reasons.  It is known, and made popular in a dinosaur movie, that some frogs possess the ability of changing gender when only one gender is represented in a population.  The second reason is that young live-bearers, including swordtails, often don't develop for several months.  Swords may grow in much later in some swordtails than others.  When they do finally start to develop, it appears that a female has become a male.

Myth: Fruit Tetras are really White Skirt Tetras that have been painted.
Status: True
Reasons: Not only is this myth true, it is worse.  Fruit, Mixed Fruit, and Painted tetras are all really White Skirt Tetras that are dipped in acid to burn off their slime coat.  They are then placed in a dye that colors them.  Many of these fish don't survive the process, those that do have a higher risk of disease and shortened life.  The dye will eventually fade, if they fish survives long enough.
    There are other fish treated in similar ways.  The Painted Glass Fish has a streak of dye that is injected into its back by a needle.  Blood Parrots are sometimes dipped in acid and dyed, too.  Few people support this process.