In addition to installing a box strike and using three-inch screws, here are some options for strengthening or replacing you door's lock:
A stronger deadbolt
Start with the foundation of the lock itself: The deadbolt. State Farm Insurance recommends the "throw" be at least one inch (the length the lock comes out from the door when it's locked), that it contain saw-resistant bolts to make sawing difficult, and a captured key deadbolt, with locks on both sides, to keep burglars from simply reaching through a window and popping the lock on the other side. For a powerhouse, check out the Ultimate Locksystem.
Control who enters and exits your house with Schlage SecureKey, a new technology that allows you to give out spare keys to those who need access, then immediately take that access away. The lock is programmed to accept two types of key, and you control which one by using a master key. Hand over a key to your plumber, and once he's gone, simply turn the lock the opposite direction and his key will no longer work. The keys themselves are very hard to duplicate, too.
With the ability to program up to eight-digit access codes, these are practically guess-proof, and like the SecureKey, access is controlled by adding additional passcodes to remove later. Plus, when someone's tinkering with the numberpad, a warning alarm sounds after enough failed attempts. Some models even sport an auto-lock mechanism that seals things up after 20 seconds, and come with a remote for locking the door from afar. As long as you remember to change the batteries (not that often), these locks are a simple way to kick security up a notch.
For some added security that makes you feel like a spy, go for a print-recognizing lock. There's no way any unwanted visitors can get in with your unique fingerprint ID, and guests can use either the passcode or the keyhole slot, which can be sealed up when not in use.
Ok, this one we don't really suggest as your most viable option. But for the DIY crowd, we felt we'd be remiss if we didn't introduce you to the Secret Knock Detecting Door Lock.