If you are using a hand-held router or a router in a router table, there's one thing you always need to be careful of to keep yourself from being injured. And that is the feed direction. The stock should always be fed into the router such that material being router is moving AGAINST the direction of the router bit. This direction should always be indicated on your router.

It's really easy to feed stock into a router in the wrong direction. And if you do this, the router will likely grab the piece and shoot it out. This can be very, very dangerous.

So whenever you are going to be using a router, make sure you know the proper feed direction before you start using the router.