I'd have to disagree with Neo on the 1 inch per gallon rule - it only works with a few different fish. For example, a dwarf puffer is only 1", but you'd need a 15-20 gallon tank to keep 5 of them, becuase they produce a lot of waste. Compare that to Dwarf livebearers, which are also around an inch. You could keep a dozen or so in a 10 gallon. It really just depends on the fish.
I do agree with Neo on the goldfish - they need cold water, while bettas need 78-80 degree water.
How big is your tank? That will really be a deciding factor on what fish you can keep with your betta. I've kept my bettas with platies, angels, cories, African dwarf frogs and otos. The angel could only be kept with my female betta though, because he would nip my males fins. Livebearers, some tetras, cories, or danios would also be nice.
Let us know how many gallons your tank is, and we might be able to give you a better idea of what would work.