It varies according to the version of video poker you're playing and that game's volatility. But the rule of thumb is to have a bankroll that's equivalent to at least two royal flush payoffs for your denomination.
So for quarters, two royal flush payoffs would require a bankroll of $2,000. For dollars, you'd need $8,000. For $5 machines, you'd need $40,000. Of course, this is for single-line video poker; for multi-line machines, multiply by the number of lines. An example: For $5 Hundred Play, you'd need $4 million.
Some experts recommend the equivalent of three royal flush payoffs: $3,000 for quarters, $12,000 for dollars, $60,000 for $5. However, Jean Scott reports that she once experienced an episode where she came close to losing the equivalent of all three royals; since then she's felt more comfortable with a bankroll equivalent to five royals: $5,000 for quarters, $20,000 for dollars, $10 million for $5 Hundred Play.
Keep in mind that this is just a rule of thumb based solely on denomination. It's important to understand that if you don't have a long-term advantage in the game you're playing, any size bankroll will eventually be exhausted. That's why you should plan not only on playing positive games, but also playing them perfectly, and software tutorials such as the new Video Poker for Winners! will take you a long way toward that end.