Bent freewheel?
 

Okay, I just bought an inexpensive mountain bike in which the original wheels were separate from the bike, but included. I got the front wheel on with no problem, now while trying to install the rear, I noticed that the freewheel is crooked. When you turn the pedals, the chain slips to the next gear, because the freewheel isn't perfectly straight up and down. Can I fix it so that it's straight again?

It's common for freewheels to wobble a little, to have the sprockets looking like they're out of true. I've never seen it be bad enough to affect shifting.
There is nothing you can do about it, it has to do with how the threads for the freewheel were cut.
Odds are it's not what's giving you trouble anyhow, that sounds more like an issue with derailer adjustment.

Hello ianbasore welcome to the forums. the wheels were not attached to the bike and you put them on? is it possible that the whole wheel is crooked? there is very little space between the freewheel and axle so ther is little chance it is was installed crooked. can you post a few pics?

Yes, is the wheel evenly spaced between both chain and seat stays?

I'm going to go with crossthreaded freewheel. Or the OP should post a video of the problem. Please.

If it's really the freewheel - and I don't recall ever seeing a freewheel that bad - You can tell if the freewheel is wobbly by just spinning the wheel withoiut pedaling. The freewheel will wobble back and forth. As the previous poster said that is not unusual (at least to a small degree) especially on less expensive bikes. Very inexpensive three piece hubs have been known fo fail enough so the flange is misaligned. I have even seen a few break loose completely. There is indeed nothing that will correct freewheel wobble other than a different hub. A cross threaded freewheel is possible but it takes a huge effort to tighten a cross threaded freewheel all the way down.

The problem is more likely to be derailleur adjustment, though - especially if it is an indexed system. The adjustment will be wrong for every gear if wrong for one. The other possibility is that the freewheel is not the proper one for the lever's indexing system.

I have never seen a wheel misalignment cause the behavior you describe (we're talking 1000's of bikes) and a very bad chainline would cause a problem on the chainwheel, not the freewheel.

I'm with operator. Freewheel "wobble" is not enough to cause derailment. Cross-threading could well be it. Any pictures of what we're speculating on?

Could be an option, didn't think of that.
Would be a challenge though to get it on crooked enough to cause shifting issues but still straight enough to go on far enough to clear the dropouts....

+1. The weirder the problem, the more helpful pics are.

It does sound like crossthreading to me, the tread on the hub might be bad.