In Finding Nemo, Nemo the clown fish escapes from his tank to the ocean, by leaping down the toilet, and swimming through the sewer. Real Life isn't like the movies. Aside from the fact that fish don't really talk (let alone speak whale), the fate of any fish that disappears down the toilet is much less pleasant than Pixar make out.
Most fish are accustomed to living in clean water. Clean water has a high concentration of oxygen compared to carbon dioxide, and no nasty chemicals in it. Sewage is anything but clean water. Sure, the water from your toilet is clean, but how about all the other toilets, being used for more conventional purposes than piscine escapology?
Very few pet fish live in cold, fresh water (goldfish being the exception, and even they live in water at room temperature). The majority of pet fish (guppies, angelfish, catfish, etc.) live in warm water, and cannot survive in water at tap temperature1. Clownfish like Nemo live in warm saltwater, so would have to contend not only with a drastic drop in temperature, but also the burning action of a hypertonic fluid. For an idea of how that might feel to the fish, try holding your head under water in the sink, and hold your eyes open.
Plumbing is not a pleasant thing for a fish to traverse. Sharp bends and fast currents cause the fish to be spun and bashed about, breaking bones and tearing off fins. It is thought that most fish die, either because of the condition of the water, or of injuries inflicted by their journey, before they reach a sewage treatment plant. It is possible that they may be killed by the flushing action of the toilet before they even leave the house.
Which is just as well, because if a fish was fortunate enough to reach a sewage treatment plant, it could expect to be ground up into manageable chunks by a shredding pump, separated out from the water, dried, compacted, and then either landfilled, incinerated, or used as fertilizer.
Please don't flush a live fish down the toilet. It's not going to have fun escapades in the ocean, it's going to die a painful death. If you take your children to see Finding Nemo, please discuss this with them before, not after, they flush the family pet.
1 - Gently reducing the water temperature until the fish dies (by putting it in the freezer, for instance) is considered quite a humane method of euthanasia for tropical fish.
http://www.jwce.com/products/30000.htm <- nice picture of the inside of a shredding pump
Thankyou to Wuukiee for corrections, and for clarifying the plot without spoilering it :)