How to remove a stuck key?
Before the key gets stuck, use graphite to lubricate the lock.

When the key gets stuck, there's nothing preventing you from using the other side of a lock (it's not the same keyhole).

If you can't gently unstick the key (forcefully removing a key may bend the pins in the lock, rendering it useless), then it's probably easiest to replace the entire lock.  They aren't too expensive, and installing them where the same size lock already exists is a simple matter of unscrewing the old and screwing in the new.