There's one constant in the gadget world: The minute you post an item that claims to have set a new record for being the smallest or thinnest fill-in-the-blank, someone will immediately dispute it. (The point was proven once again in discussions stemming from the MacBook Air.)
So the only thing we dare say is that, as of this writing, Akihabara News is reporting what it calls "the slimmest waterproof phone ever made." The 3G handset in question is the Fujitsu F705i, which measures 13.7 millimeters thick, or about 0.54 inches.
There are most certainly other phones that are even slimmer, but how many can be plunged in a meter of water for 30 minutes and keep on ticking? No, we don't know why one would need an ultra-thin phone to do that--or any phone, for that matter. Maybe it's some weird fitness regime needed to maintain its svelte figure.