Your poker bankroll is the amount of money you have set aside to play poker with. Some players can easily add to their bankroll from outside sources while others have no way to add if they lose theirs. If you fall into the latter category, it is very important to not play at limits that exceed your bankroll.
One very important point you should know is that until you become a consistent winner it doesn't matter how big your bankroll is. The only thing that will matter is how much you have to lose. For this reason, the information below is written for you, assuming you are a winning player overall.
The first rule is to not confuse bankroll and buy-in. A buy-in is the amount you sit down in a game with or the entry fee in a tournament, not the entire amount you have available to play poker with over a period of time. For example, you may have a bankroll of $10,000 to play 15/30-limit holdem. If this were the case you would probably buy-in for between $500 and $1,000.
I have seen poker bankroll size suggestions ranging from 200 times the big bet at the level you are playing at ($800 at 2/4) to 300 times the big bet ($1200 at 2/4).
My recommendation, particularly for holdem, is to start with 300 times the big bet. I play much better when I have this cushion. I have played at levels that I had much less than 300 times the big bet in bankroll and it sometimes hurts my play.
This is a psychological hurdle but when reduced to facts it makes sense. 50 times the big bet is a common downswing, even for professional poker players, and nothing to become too concerned about if you are still playing well.
However, if you start with only 100 times the big bet, if you are down 50 big bets you have lost 50% of your bankroll. If you had started with 300 big bets and are down 50, you have only lost roughly 17% of your bankroll.
If you are a very sound Omaha/8 player, you can play with a 200 big bet bankroll. This is because Omaha/8 is a much more mathematically direct game than holdem, or in other words there is less short-term variance or luck.
Because of the short-term variance in holdem, even professional players may see a 200 big bet downswing at times. For this reason, that extra 100 big bets may keep you from being forced to drop down a level before the cards turn in your favor.