Megapixels: I can't remember what the current standard is. If you get a good camera IMO you don't need maximum Mp, however. My 3.2 MP Canon takes so much better quality photos (given the same environment) as my new 5MP crappy underwater camera. If you are not planning to print your pictures massive (10x13 or bigger) you shouldn't have a problem, whatever you get (unless you get something crazy like a 1MP).
I'm sure someone else can come up with more than me, but:
What else is important to look for in a decent camera depends on what you want it for. For instance: The last camera I was looking for, my two biggest items on my list were lots of Zoom (for those shots of wildlife that is far, far away), and manual focus capability (because a pet peeve of mine is when I'm trying to shoot through trees or something and the camera won't focus on the thing I need it to focus on).
My brother was looking at cameras at about the same time but he really wanted something pocket-sized to take when hanging out with friends. Low light settings were important, but zoom not so much!
Keep in mind if looking at zoom - Look at OPTICAL ZOOM only. If you use digital zoom, image quality is greatly reduced (as if you had just taken the non-zoomed photo and cropped out that little part).
And as I said, my mom was looking for easy use and a little zoom to get photos of my brother doing sports, where she is rarely in close range.
Some things to consider:
Batteries come in Lithium-Ion (rechargeable) and standard AA, AAA, etc. I like rechargeable and the ones made by the camera companies last for at least a couple days for me. I have one that I bought as a back-up that was cheap, that lasts about 4-5 hours, but that's usually all I need it for. I like not having to buy new batteries all the time (and have been known to spend extended periods where no fresh batteries were available for purchase), but if I forget to recharge (happens rarely, since I have 2 batts per camera... one is nearly always charged) I'm out of luck. My mom prefers AA's because you can buy them anywhere if they die somewhere. What do you find more appealing?
I don't know how easy it is to find smaller point and shoots with a viewfinder in addition to the LCD screen these days. One of these is essential IMO, firstly in the case of someone used to a 35mm who may take time to adjust to holding the camera differently to compose on the LCD, and also in high light situations, where the LCD gets a lot of glare. My mom said that when she went most of the cameras were all LCD.