Exactly the same thing happened to me this morning. Later in the afternoon it was working again.
Same thing happened to me over the weekend. Found my first cache on Thursday (go me!) with the iPhone app, and wanted to poke around and find more on the weekend.. and then the crashing started. I uninstalled/reinstalled the Geocaching app, but that didn't fix it. Then I read about uninstalling/reinstalling winterboard, but I don't have that installed. I did have BossPrefs installed though. I did a bit of poking around and found a button in the BossPrefs "More" menu called "Fix User Dir Permissions". I hit that, and bam, the Geocaching app worked again.
I don't know if it was just crazy timing and I was crashing because of the server issues other people have talked about, or if it was because there was some kind of permissions problem with the old/corrupt/whatever database for the Geocaching app on my phone, but clicking Fix User Dir Permissions in BossPrefs worked for me.