I prefer to use a multiple of the Big Blind rather than a number of buy-ins. That said, with the current most common structure (buy-in equals 100 BB's), the result isn't really much different.
I keep my bankroll above 2,000 x Big Blind for the level I'm playing at. I drop down if my bankroll drops to 2,000 x Big Blind for the next lower level. That's the plan anyway. The reality is that I usually can't stomach my bankroll shrinking by more than 500 or 600 x Big Blind at any given level, and will drop back a bit earlier. I'm just not playing my best poker when I'm thinking about the hundreds of dollars I've tanked

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As you can see, with a 100 BB buy-in, this equals the normal 20 buy-in recommendation. I think you need a biggger bankroll (in terms of buy-ins) for games with a smaller buy-in relative to the Big Blind (eg. the 'old' party structure). Similarly, if you find a structure with a large buy-in (maybe 300 x Big Blind), I don't think you need as many buy-ins.
My reasoning: In NL, the size of the pot and the style of your opponent should be driving your betting decisions, not how much money you have in front of you. The size of the pot is driven by the size of the blind, not the buy-in. If you are the type of player where your entire stack is regularly at risk regarless of pot size, I recommend limit

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There's my 2 cents worth.