My toilet has been running for 3 days. I've tried everything, including cleaning out the tank to remove any deposits that may have been the problem. I've had this problem before, and I've always fixed it. I would just shut the water off, but whoever installed it didn't put a shutoff valve on the water line (as far as I can tell). PLEASE, someone give me some advice!

Ok, it can't be that hard to figure out so let's try it from the top.

Is the flap seating properly over the drain hole allowing tank to fill up?
Is the water ball at the right water level to turn off the water once the tank fills up?
Is the water able to shut off when the big black water ball is in the up position?
Is there a crack in the white filler tube preventing the tank from properly filling up all the way.
Does the tank fill up completely or part way?

Please go see if any or all of these items are the culprit and then tell me which one it is. Ok?

My toilet doesn't have a ball, it has a rod with a black 'floatie' which is basically the same thing. Its at the same level as always.
The tank is actually filling so much that the water runs out through the white tube which is he only thing keeping me from having a huge mess on my hands.
The 'floatie' rises all the way, and the water just keeps running.
Like I said, I've been able to fix it before, just not this time.

Sounds like the left side of the toilet needs totally repaired and replaced. Go turn off the water totally or you'll have a mess. You'll have to anyway to replace this entire part.
It's the water intake tube that went. It's where the black floatie thing fits into. If you don't have the proper tools to complete this project like huge pliers - then you'll have to call a boyfriend who has the tools or call a plumber. Go to Lowe's or Home Depot for the part.

The part is not that expensive but doing it right is the hard part.

Yeah, that's what my husband and I thought too. My only thing is that I believe my shut off is under my house and I'm not quite sure where, and he's at work. Thank you so much for your help!:D

You're most welcome. If you have a hubby then I'm sure he can fix it. If it had been the drain thing on the right I was going to give you a quick tip how I fixed mine without having to take the whole shebang apart and fixed it for 48 cents.

Good luck and happy plumbing. I've been a toilet expert since age 6 having successfully taken apart my parent's toilet. I also took apart my Cinderella watch also but could not get it back together again. At least I know how both of those things work now. LOL

Most toilets have a shut off, stop, located on the supply pipe under the toilet, does yours? If you pull up on the black can does the water stop? Most problems require adjustments or a replacement diaphram, raely total replacements unless you aren't wanting to become a DIY plumber.