I'm a big fan of the Canon Powershot S and A series. I've got a 5-year old 3mp S30 that has served me extremely well- the new cameras out now are high in megapixels and have gotten extremely cheap. I've got a 7.2mp Sony with a 12x optical zoom I use at work, too, but that's too bulky/expensive for everyday use. I have a miniature solid-state camcorder I got for $120 at radio shack that's also a 3mp camera; it doesn't have a flash or optical zoom, but outdoor daylight photos turn out pretty good. It's a lousy camcorder, too, but it's just so freaking small, I use it all the time.
For everyday shooting, 3-5mp is fine and there are so many choices it's almost impossible to narrow the field based on options. I'd recommend something with a 2-3x optical zoom and one that takes movies so you can use it as a camcorder. Beyond that, it's all preference- go into the store and take 'em all for a test drive! Then go home and order online for significantly cheaper