[DMoogle]

For limit, think of your bankroll in terms of big bets. Standard *minimum* recommended bankroll is 300 big bets. Example: $10/$20 limit would require a minimum $6,000 bankroll.

For no-limit, think of your bankroll in terms of buy-ins, where one buy-in equals 100 big blinds (which is usually the maximum online poker sites let you buy in for). Recommended *minimum* bankroll for NL is 20 buy-ins. So in a $10/$20 NL game (also called $2000 NL), one buy-in is $2000. The recommended minimum bankroll for $10/$20 would be $40,000.

EDIT: Also I should add that as your go up in limits, your relative bankroll size should become larger to compensate for tougher games with higher variance. For example, $10/$20 NL is considered high stakes and most people who play there would agree that a 20 buy-in bankroll is far to small... something like 50 buy-ins would make them feel more comfortable. Of course, bankroll management in general can depend a lot on your ability to move down after a downswing. If you have difficulty playing lower limits seriously, then you need to have a larger bankroll at the limits you play at to compensate so you won't have to move down after a downswing.