Hi there.
I own a 2002 Saturn sl1. THe engine has stopped on my while driving twice now. The first occasion i was pulling into my house and as I applied the brakes to stop it shut down... There was no stalling or nothing, the engine just stopped working. The lights and everything were still on. I turn the car back on with no problems, engine turned over fine and everything. No MILs were on. I push the brake pedal again... and the engine then turns off again.

The second time i was pulling onto a street and hit a bit of a bump and the engine just stopped completely. No stalling or nothing. Again, the lights and everything were working. Anyway, i turn the key and the engine turnsover fine and away i went. I was using the brakes, highbeams etc all the way home.
Problems?
btw, this is probably unrelated, but a two weeks ago nothing would turn on (no lights, starter wouldnt even click), but after I replaced the positive terminal for the battery cable it worked fine.
also, i ran a diagnostic test on it and the cars computer has no codes on it...

 

If I were to hazard a guess, I'd start looking for a cracked vacuum hose