Flash can and will crash your browser at times. Watch your CPU usage spike whenever you load a page with flash – by running someone’s crappy code, there goes your battery life. This is especially bad on some platforms (linux, PPC macs). I can only imagine it would be much worse on the iPhone.

Used sparingly and for certain things where it’s the only option (games, video) it’s fine.

Outside of that, flash breaks a whole lot of what is good about the web. It’s not searchable – text you may want to show up in a search engine dissappears into a black hole if your site is all-flash. This also causes problems with accessibility for the blind.