hour and the car starts. I was driving and the dash lights started to go dim and the anti-lock light came on. I got to my destination about 1 mile later and went to restart the car and it was completely dead. After about an hour, I went out so I could jump it but it started right up without even opening the hood. I started driving, got about 5 miles and the lights started to dim again, the anti-lock light came on, then the airbag light, then the car died while i was cruising (I was going about 30 and didn't have my foot on the pedal). I had to leave it on the side of the road for the night. I went back the next morning and, again, it started right up. I drove it about a mile to my work and took the battery out and it's now on the charger. The terminals had a lot of corrosion on them so I cleaned them as well as the cables. I am waiting for the battery to charge all the way but I doubt that it's the problem. Could it have been the corrosion? I looked at my cables and they "look" to be fine. Help.
Could it be the alternator? Why would it die while driving yet after some time the battery charges itself enough to start the car again?

Dead on. It's the alternator. No other possibility.