Fixing this was on the top of my list when I heard about Sugru (Sugru.com). The fix is working great so far!
I couldn't figure out what to call the little piece that moves in and out when you turn the handle. I Googled it and decided that the "bolt" is a good name for it, so when I refer to the bolt, this is what I'm talking about.
Step 1: Materials
A door that won't stay shut (because of a wide gap).
I used a tiny bit for another hack, but 1 (5g) pack should be the right amount. I was surprised how closely the green matched our oh-so-green trim.
You can buy Sugru here: sugru.com. You can do so much with this stuff, it's worth buying a big pack.
Step 2: Prep the door frame
Note - If the strike plate is exposed (mine is painted) and it's brass, it probably won't stick. You might be able to stick it to the door frame though. I'm not sure what other metals have problems, but brass is one. I wasn't sure if it would stick to the paint but it worked for me!