I run a small shop that fixes Droids and this proximity issue drove us crazy when we first started fixing the screens. After a lot of research and trial & error, we figured out what the main cause is.
Basically, it's a design flaw in the original Droid that was addressed in the Droid 2. The problem is the little rubber grommet that is supposed to separate the proximity sensor sender from the receiver. If this isn't seated perfectly, the proximity sensor will not function properly. One of two things will happen:
1) The sender or receiver will be partially covered and the screen will never go off while making a call. This is what creates the annoying problem of your face accidentally hitting buttons.
2) The grommet doesn't properly separate the sender from the receiver and the sender light reflects off the inside of the screen directly into the receiver. In other words, the phone always thinks it's against your face even when it's not. In this case, the screen goes black immediately when you start a call and frequently, due to a software bug, will not come back on even after your call is over.
A few things to suggest:
1) If you are considering buying a Droid, get the Droid 2. Motorola fixed this issue on that version.
2) If you already have a Droid and it's under warranty, take it back to the store and get a new one. Preferably, get them to upgrade you to the Droid 2 (which they may or may not do).
3) Try the Screen Suite suggested by appsbeyond above. I've actually never tried that and glad to hear about it and I'll definitely try it out.
4) If your phone is no longer under warranty, you can try to disassemble the phone yourself and put a small piece of neoprene on the underside of the screen in between the sender and receiver "holes". This little divider should get things operating properly again. If you're not comfortable pulling your own phone apart, find a 3rd party out there to do it for you. They shouldn't charge you more than $50 to do it.