I use an Olympus TG5. As Crossbolt mentioned I have it hanging from a lanyard around my neck. It is Waterproof and shock resistant. It also captures colors better than any digital camera I have owned. I can take pics while riding. I grab it with my left hand, turn it on, point and shoot. I don't look at the view screen while riding, I keep my eyes on the road. I get a lot of pics this way that I otherwise wouldn't get. Even when I stop it's a lot quicker and more convenient that a phone camera is because its right there and ready to use.
The hardest shots to get are over the shoulder shots of the riders behind me. Most of those used to be junk but I have gotten much better with practice. Since I normally lead the group rides I go on, I have been taking a lot of over the shoulder shots.
Here's a pic taken while riding.
One taken over the shoulder to get bikes in the pic.