I carry an old Canon S500 Elph everywhere. Its just a 5MP and very simple, but includes a video mode, simple EC, and some other goodies. My sister has a newer model from this series, and shutter lag is greatly reduced and it has IS. Great little cameras. If I were to get a new compact digicam, it would be one the waterproof OLY models:
Olympus | Stylus 850 SW Digital Camera (Black) | 226325 | B&H.