There is much debate about tank size. I prefer bigger, a 10g per fish setup, but it seems that the majority on this site keep a single betta in 5g's of water in various set ups. As Matt said, a 1 gal bowl/tank is the minimum. I think of it being like living in a tiny 2 room studio apartment vs. living in a full-sized house in the suburbs. I want to live in a house, and I do my best to provide my fish with the same accomodations. :)
Also, you can get a 10g tank at walmart for 10$...the 1g bowls run about 6$...I'd just spend the extra 4 bucks and get the big one. ;) The other benefit to getting a larger tank are these:
-a 10g can be divided two ways and you can keep a second betta (yay!)
-a larger tank is easier to keep clean, you can filter and cycle it, which will make your life so much easier and improve the health and well-being of your betta as well
-with a big enough tank you can keep some tank-mates (either other betta-compatible fish or snails) which gives some much-appreciated interaction to your betta. Which, again, improves the quality of their lives.
You hold their entire universe in your hands. Everything they get they get from you. It's your responsibility to take care of them and to make their lives as rich and fulfilling as possible. :)