peekabot is not a simulator, only a visualization tool, and to some extent a tool to control your robot interactively. It's a good match for use in conjunction with a simulator without its own visualization, though.
MRPT doesn't have a (complete) simulator AFAIK, only algorithms, interfaces, drivers and its own log format. Besides that, it looks neat.
OpenRAVE might be worth checking out if you're interested in planning.
Gazebo wasn't really mature and stable enough last I tried it (~1 year ago). Might be worth to check out though.
Stage is simple to use, provided that you need only a 2D simulator without dynamics.
I've used both ODE and Bullet for robotics simulations, and both worked okay although I would recommend ODE.
To get a more definitive answer you need to refine your requirements -- i.e. are you looking for a simulator only or something more like ROS, do you need a 3D simulator with dynamics or only 2D, how accurate must it be, what sensors do you want to simulate, etc.