Other workarounds
Tuning problems due to bending or whammy bar use are caused by two things: strings slipping when and where they shouldn't, and strings not slipping when and where they should.
Two specific problems I've run into are strings sticking in the nut, and the twists on the ball end of the string collapsing when the string is bent.
Jeff Teel already covered this, but... sticking at the nut can be reduced by installing a Graphtech nut, or by using some kind of lubricant. If your nut is black, ordinary powdered graphite (or even pencil lead!) is a good choice. For white nuts, you can buy a powdered Teflon lubricant at hobby shops. Or try using good old 3-in-1 Oil -- just a dab applied with a toothpick should be plenty, any more will just soak into the wood.
If you're buying a new guitar, and you don't need a 3-on-a-side traditional headstock for appearance's sake, go for a headstock design that pulls the string straight through the nut.
As for the ball ends slipping, you can either solder your strings if you're cheap and have time to do this at every string change, or you can buy "tremelo reinforced" strings. I've used GHS Tremelo Boomers with great success, and D'Addario offers pre-soldered strings. Both are only slightly more expensive than their regular strings.
If you use traditional tuning pegs, how you wrap the string makes a big difference. Any of the guitar setup/repair books will have tricks for locking down the string on the peg. Or see
www.frets.com.
Last, if your guitar has Sperzel locking tuners or similar, you should wrap the bare minimum of string around the tuner to get to pitch. The less string on the tuner, the less likely it is to slip and stretch when you bend or dive-bomb. The instructions that came with my Carvin say 3/4 of a turn max! I get there by pulling the string taut by hand before locking down the tuner.