Plenty of folks here are running tanks at or under 20 gal. I would venture to guess that most start the hobby in the 5-10 gallon range (or, heaven forbid, a bowl).
I've got a 1/2 gallon "tank" on my office desk that's outfitted with a 7W 7200k light (I removed the reflector to reduce the output to a manageable level), a Red Sea HOB nano filter, 1" of Eco-Complete substrate, a java fern and a few small cuttings of Anacharis, and a single male Betta. The lamp keeps the water about 6 degrees above ambient (81, in this case). The filter only has simple sponge media, but it works quietly and has adjustable flow. The live plants, porous substrate, and sponges together should make for a nice biological filter.
The whole setup is only 7" x 7" and about 14" tall (Counting the light, which is about 7" above the tank). I paid $21 for the tank/light/filter.
While you can find smaller vase-type setups, they are really too small for even the smallest of fish.
If you look around the gallery, you can find some really gorgeous five and/or ten gallon setups.