No. The breakers are sized for the wire that was run. If you put two circuits into one breaker a single wire of the circuit (which was rated to carry 15amps) could now carry 30 before the breaker blows. This can lead to melting wires and fires.
You could combine both circuits to a single 15 amp breaker, but it would likely be overloaded. This might be a possibility if both circuits are very lightly loaded.
What you can do, if your panel supports them, is get a tandem breaker - which will have two 15 amp circuit breakers in a single unit that takes up the same slot as a single breaker.
Otherwise you will need an electrician to setup a subpanel - they will add a second panel which connects to the first, and move some of the circuits to this new panel to create room in the main one.