As usual, this one size fits all does not fit so well. A more accurate measure of needed bankroll is to calculate based on one's win rate, the standard deviation of that win rate and risk tolerance. Here conventional advice says a 1% risk of ruin for professionals and 5% for non-professionals. Even if one takes the 1% risk of ruin, this may lead to significantly different bankroll requirements than 2000 big blinds. For example, a player with a 5BB/100 win rate with a standard deviation of 50 needs only 1,151 big blinds per level, which is quite a bit less than the 2000 big blind rule. If that player has a game with more variance, such as a standard deviation of 80, then 2947 big blinds are needed, which is quite a bit more than 2000 big blinds. (If you are interested in the formula just run a Google search; you should also come across a website that calculates your bankroll requirement for free.)
The 2000 big blind rule is inexact, but the idea behind it is sound. The nature of the No Limit game means that variance is high. Each hand you play could be for your entire stack. A 2000 big blind rule protects you against a run of bad luck. Usually, you have to get very unlucky to lose it all if you are a winning player. It isn't impossible, of course, just unlikely (for the average player). The 2000 big blind rule allows you to comfortably play at the next level, knowing that a bad run won't take out your bankroll. Of course, you can also use the bankroll formula with standard deviation, win rate, and risk of ruin to play with confidence that you won't go bust at the next level. This confidence, or more precisely, comfort, is the key factor for the amateur (and the pro). How comfortable you are, however, is dependent upon how much risk you are willing to tolerate, and having conventional rules or a formula around, may not swing it for you. You have to sit down and ask yourself how much of a loss you can take and still maintain your A-game.
Even if you were a very good player with a very high risk tolerance, it would be foolish to risk your entire bankroll on one or even two tables. Short-term bad luck can wipe out all your hard work. Even if you save some you may be under bankrolled at your previous level.
For example, say you play the .10/.25 game, have $500 and decide you are good enough to beat the .50/1 NL game; indeed, you may be. Unfortunately, some bad luck befalls you, and you lose one buy in w/ K-K vs. A-A, another when the situation is reversed but the K-K sucks out on the river, and the final time when someone bluffs a flush draw on the flop and you call with a set only to drown at the river again. In a mere hour your $500 is down to $200 and you retreat back to your old game, but the bad luck continues here and you lose 4 buy-ins over 2 days. Again, just bad luck; you play well, but the cards don't care if you are the better player. Now your bankroll is only $100 and continuing to play at your current level is a precarious situation so you may have to drop down again just to rebuild an adequate bankroll for your normal game. The moral of the story is patience. That beatable .50/1 NL game will still be there. Yes, play within your comfort level, but don't take too much risk. That's the whole point behind risk of ruin or saying that you need 2000 big blinds for the level.
While your entire stack is at risk in NL, a better assessment of what you are likely to lose at the next level is your standard deviation. Standard deviation is a measure of the distribution of your wins and losses around your win rate. The lower the standard deviation, the less volatile your game tends to be. There is no ideal standard deviation rate. Rates vary based on the style of game that one plays. Loose-aggressive styles have more variance and hence higher standard deviations than do tight-aggressive styles. The number that matters at the end of the day, however, is win rate, and the loose-aggressive player may play this style well and have a higher win rate than a tight aggressive player. Daniel Negreanu, for example, has (I would guess) a higher win rate than I do, but I'm quite sure his game involves more variance than mine. The higher your standard deviation, the higher the bankroll you need to move up, because you play a game with more risk than the tight player.
If you calculate standard deviation yourself, based on the number of hands you play, and the amount won or lost, be aware that if you just record the total hands and total wins/losses even though you play multiple tables, then you will have a lower standard deviation than you would if on a program such as Poker Tracker, which counts each table one plays at as an individual session. Playing multiple tables will actually reduce variance, as risk is spread out (much as investors buy multiple stocks to reduce their risk). I think this is a slight flaw in the tracking programs, though I think their many other benefits outweigh it. Thus, if you plan to play multiple tables at the next level, you can slightly lower your standard deviation number if you obtain it from a tracking program, but only slightly; it's still fairly close and you don't just want to guess.
Okay, now let's get to it. Two standard deviations usually encompass 95% of possible results. Thus there is only a 5% chance that you will lose more than 2 standard deviations from your win rate in a particular session. For example, let's say your win rate is 5BB/100 and your standard deviation is 50BB/100. If you are considering moving up to .50/1 NL then you can reasonably infer that there is only a 5% chance that you will lose more than $95 over 100 hands (5BB- (2x50BB)). If you take 3 standard deviations then you encompass over 99% (it is over, but I'm just going to use 99%) of the expected wins/losses. In this case you have a small chance of losing over $145. Decide what sort of risk level you are comfortable with, 5% (2 standard deviations) or 1% (3 standard deviations). That is the amount of money you need to risk playing 100 hands at the next level in addition to what you feel comfortable having on hand to play your current level. Continuing the example, if you are comfortable playing .25/.50 NL with $800, and want the 1% risk level, then you need to win $145 more to take a shot at the next level.
You can get a more accurate assessment if you convert the win rate and standard deviation into the number of hands you normally play. Thus if you normally play 200 hands in a session, then you would want to convert your win rate into BB/200, then resolve for standard deviation and run the numbers again. Yes, you can just double the numbers. This will tell you how much you are likely risking by playing at the next level in a normal session. In our example, the risk is $290.
A lot of players tend to think about levels of play in sedentary terms. They stay fixed at a particular level for long periods of time and view moves to a new level as relatively permanent. I prefer a more fluid approach working from your comfort level. Kristy Gazes recommends moving up in levels if you win 3 consecutive sessions and conversely moving down in levels if you lose 3 consecutive sessions. Now I would add your comfort level and risk factor. Once you have determined how much risk you can tolerate at the next level, and have acquired that much in addition to your comfort level at your current level, then take a shot when you win 3 consecutive sessions. You aren't moving permanently to the next level; you are just taking a controlled shot. If you are a solid winning player, you will likely win at the next level, but of course, there is the possibility of loss. If you take your shot and lose, you can go back to your old level and rebuild enough bankroll to take another shot. Instead of "moving" levels, you just take shots. If you win in your first session, play another. If in the second session you lose all that you won in the previous session; i.e., you have less than the money you have set aside to risk at the new level, then drop down to the old level again and rebuild to take another shot. Rinse and repeat.
There are quite a few advantages to this approach. Risk to your bankroll is quite low. You may lose all of your table buy-ins but that is unlikely unless you have a really high standard deviation. Whatever your standard deviation is, you bring enough to be prepared to lose. This means that you should be able to play your normal A-game instead of playing with scared money. Thus this approach keeps you within your comfort level and protects you mentally; giving you the best chance to play well. Playing at a new level is a transition and will have some bumps in the beginning as you get used to the new bet sizes and quality of opponents, but since the transition to the new level will be drawn out and extended, you reduce the shock that might normally be experienced. Play at a higher level will be better than your previous level and this will improve your game as you develop new plays and new reads. This is an advantage over your opponents who are waiting around to build up 2000 big blinds before venturing up to the higher level, unless you require a higher comfort level than 2000 big blinds, and if you do, that is okay.
Move up gradually and be prepared to move down if things go badly. Don't let your ego get in the way of playing disciplined poker and practicing sound bankroll management. Take controlled shots at the next level. When have you officially moved up? Tough to say. You might say it is when you reach a comfortable bankroll level or more precisely when you feel at home on that level. I would say officially, that you should stop thinking in these terms. Be fluid, move up and move down without any thought as to this being a BIG STEP or an admission of FAILURE. Just concentrate on playing good poker. Stay disciplined and within your comfort level and your transition to the next level up will be smooth and painless.