You can bet anywhere from 1 to all 38 numbers on an American roulette wheel. This includes a straight up bet on any number 1 36 and bets on the zero and the double zero.
You can cover any six numbers from two rows called a six-line bet on a line that intersects them and the payout is 5-1. You can bet on any of the vertical columns and the payout is 2-1. There are also squares for the numbers 1-12, 13-24 and 25-36.