My favorite is the new logitech
Logitech Pocket Digital 130. 1.3mp, It is the size of a thick credit card, metal body, has a limited flash. No batteries - rechargeable from USB - which could be either an advantage or disadvantage - I love it. Optical viewfinder, no LCD back. Very fast to operate to catch that fleeting shot, and small enough to have with you always. A big improvement on the previous model, which is, however, thinner. £80
The Fujifilm Digital Q1 looks like the analog version (funky round styling) and is 2mp, with limited flash. Unlike the Logitech it has a LCD back. Digital zoom, AA batteries, plastic body, takes movies and an optional extra media card. It is nice enough, but it is so slow response compared with the logitech. For example, a button-press for power on takes maybe 3 seconds or more to start, during which time the picture has moved. The same when operating the shutter for people on the move. No optical viewfinder, so you just have to have the back on and run down the batteries. At a rough guess, they last long enough for about 200 pictures. £83 plus optional extra memory.
I used both on a recent skiing holiday. The Fuji was better in that it offers white balance for snow correction, but it was a lot slower to use, and the little buttons are difficult with gloves on. The fact that the LCD is on all the time means you want to turn it off, but if you do you can't boot up quick enough for those passing moments. The logitech is basically a joy for speed and ease of use but could be limiting if you don't have a USB port around for charging after a 100 or two pictures. On both of them the flash is very short, making the useful range something like 4 to 6 feet. On balance, I'd have the logitech and something more serious for better indoors and planned shots.