Here are a few recommendable point-and-shoots and the reason for recommending them:
• Fuji F20. Tiny size, good image quality, and good low-light performance.
• Nikon S10. Unusual and handy form-factor.
• Canon A640. AA batteries, articulated LCD screen.
• Casio EX-S600. Simple controls, decent shutter lag, not too expensive.
• Olympus 770SW. "Shockproof, freezeproof, waterproof."
• Ricoh RDC-7. Very slim, doubles as voice recorder.
• Panasonic Lumix DMC-LX2 (a.k.a. Leica D-Lux 3). Image stabilized, 16:9 ratio, good lens with true wide angle, fast at the wide end, shoots RAW.
Any others anybody wants to recommend?