Click images for a larger version
Deadbolt lock security varies greatly due to age, manufacturer and quality of the lock. All deadbolt locks should have a 1" long bolt that, when fully extended, locks (dead bolts) in place. Prying on the bolt should have no effect if the bolt is well designed and installed properly.
What you can do - Remove the lock from the door and take it to a lock shop to have the cylinder(s) rekeyed. Caution: If you try to replace your lock with a new style lock, the holes in your door and frame may not be the same sizes.
If you can see 2 standard screws on the inside plate (as shown in the second image above), you have a simple design. Remove the screws and remove the lock slowly. Don't drop any parts. If you have one-way security screws (as shown in the third image above) you can usually loosen them by tapping the head of the screw around counter clockwise with an old chisel and hammer. Then use a pliers to finish taking out the screws.
If you do not see screws on the inside plate, your lock may have hidden screws. Some lock manufacturers who have hidden their screws are Medeco, Arrow, Schlage, and Lori.
Arrow double cylinder deadbolts (keyed on both sides) require you to insert the key in the inside key cylinder. Turn about 1/4 turn to open the access holes to the screws. Use a thin phillips screw driver to go in the holes and remove the screws.
Medeco locks have a cover plate over the screws. There is a thin wire in a groove in the inside plate. If a single cylinder, loosen the set screw in the under-side of the thumbturn with a very small allen wrench. Remove the thumbturn. Find the end of the wire and remove the wire from the groove with a tip of a knife (or something with a point). The brass plate should come off. Now you can see the screws to remove the lock.
Lori locks are similar to mortise locks. The outside cylinder and possibly the inside cylinder screw into a housing. You will find the set screws by removing the face plate of the bolt on the edge of the door. There is an opening on each side of the bolt. You should need a 5/64" long allen wrench to reach and loosen the set screws. Then unscrew each cylinder.
Schlage older double cylinder deadbolts may have brass caps driven into the heads of the screws. Take a small chisel and tap around the line of separation between the cap and the screw. It should loosen up and pop off. If not, you may have to drill the screws off. The B600 double cylinder requires you to pry off the inside face plate carefully in order to re-use it. The first image is of the screw and cap apart. The second image is of the cap in the screw head.
What a locksmith can do - An experienced locksmith will have the tools to remove the locks and re-pin (rekey) the cylinders in your house or in his truck and then reinstall them.
Since deadbolts are the serious security on your doors, he should advise you of any weakness to your door or frame. If your lock is older or of poor quality, he may recommend a better lock.