I just purchased a '98 Monte Carlo. Come nighttime, though, the tail lights weren't working. After replacing the fuse once, it blew, and after replacing all the side light bulbs, I replaced it again. It blew. Is this a typical problem, or what wires might be shorting my poor car's fuse box?

 

It doesn't necessarily have to be shorting at the fuse box, it can be any power wire in the tail light circuit. Without a wiring diagram, I would check whatever wires you can see going to the taillights for exposed wires, black spots, pinching, rubbing, etc.

 

another thing to find out is to see if it has a bad ground wire in there any where. Also if has been hit in the tail end to cause the wires to become broken if so replace or fix them and make sure they are in teh right places and connected good .
Clean the ground wires locations where they hit the body at the tail lights. mos tof the time it is in the trunck under the carpet by the trunk latch.

 

A loose ground wouldn't cause a fuse to blow, it would just cause the circuit that it grounds to not work at times. And even if the ground wire is shorted, it wouldn't blow a fuse. Power has to short to ground to blow the fuse.