I've been using MyEclipse - a cheap wrapper around Eclipse that does one hell of a lot.
It can start and stop Tomcat and deploy to it (along with many other app servers).
One quibble, why does it include JSTL 1.0 versions in new web-app projects? (This took me for ever to hunt down...) Freaking stupid errors about not being able to understand the URI...
God damn! Anyway, back on with the show. Eclipse rocks, and my experience with it wasn't too great before paying 20 quid for MyEclipse, but in general, I'd recommend it to anyone wanting to start out with Eclipse with web apps.