[Doc]

I wouldn't describe that as overly cautious Jez, in fact it is moderately aggressive!

The variance in limit poker is generally (and I believe correctly) seen as lower than that at no limit. Similarly the variance is larger for short handed play, and larger for aggressive play (you or your typical opponents). Also, a lot of people don't realise that when you multitable - your variance goes up (and that is even before taking account of the fact that your average profitability per table tends to drop as you're trying to concentrate on more).
An often quoted figure for limit poker (playing full tables) is that you want 300 BB (big bets, where 1Big Bet=twice the big blind) PER TABLE.

So if I want to 3 table some $1/$2 tables in limit poker (the buy-in would typically be $50 for these tables), I want a bank roll of $1800. If you were playing 6 handed tables I'd double that, so more or less $3500

The equivalent for NL might be a $5K bankroll if you want to 3-table 15c/25c blinds on 6 max tables

No doubt there'll be a string of posters who will think this is stupidly cautious and will talk about how they play these tables with a $200 bank, but as you've indicated above, it is more a case of when not if they go bust. Everyone gets bad beats, everyone gets cold decks and everyone tilts (to some degree) at some stage. You need the bankroll to ride those out.