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.