It's debatable. There's a lot of controversy behind this issue, most popular belief (and the one I believe in) is that the small tank will stunt their growth and lead to a shortened lifespan and deformities. A side of it you will hear on the forums a lot is that if you keep a big fish in a small tank, although its skin stops growing, its organs still do, which causes a slow painful death, though there isn't much research backing this one up.
Ultimately, if your tank is not big enough to support your desired fish's full grown size, don't get the fish. Regardless of how much you want it, if you'll have a bigger tank later, etc etc etc.
You do have to sample the supposed knowledge out there on a particular fish, you will get varying results sometimes.
For instance my father got a Pictus Catfish for his 29 gallon tank and a few people have told me they require a 4 or 5 foot long tank but I've read more than a few places that the minimum tank size is 20 gallons.
That's because pictus catfish prefer to school in groups of 6 or more, and can get 6-8 inches long, and never stop moving. I have never seen an inactive pictus catfish. They make danios look like lazy slugs. Assuming you want to support a single 6 inch pictus catfish that is left inactive and stressed out, yeah, 20 gallons seems like a good minimum. If you want a keep a healthy school of these very active (and somewhat sensitive) fishes, 4 feet is much more preferable.
Also, I've read in more than a few places that you should rinse your filter pads under warm tap water once every 2 weeks and replace your pads once a month. That doesn't mean I do it.