Electrical Overload? causing stall

Hello, I have a 2000 V6 3.8L 5-speed with about 107k miles. Yesterday on the way home from work while driving in 2nd gear at a steady pace on the freeway my car suddenly turned off without notice, but of course it was in gear so it just slowed and jerked a bit and turned back on just as quickly as it turned off. A few minutes later it did this again in 3rd gear. Earlier that morning on the way to work the headlights had been dimming significantly for a split second at a time, but I didn't think much of it because the heater and radio were on, and it seemed like it was doing that whenever the fan started.
I just recently replaced my spark plugs/wires only a couple hundred miles ago.
Any ideas what the problem is?

Thanks, that is the next thing I was going to check out, but I haven't had a chance to do it yet. Can alternators fail intermittently like that? I had one go out on a previous car, but it was more gradual and didn't behave like this.

Got the electrical system checked at the hardware store, and after difficulty getting the tester to acquire good connection to the battery terminals, the charging system and battery checked out fine. I've been having problems with my battery cables and terminals ever since I replaced the battery and the terminals because they were so corroded, so I think that they might be the cause. I'm planning on replacing the whole set of cables with stock ones from the dealer because they just don't sell anything at the auto parts stores that works very well. Thanks all for your input.