My 2006 Jetta every so often will slow drastically down or sometimes totally stall when I try to accelerate, especially on hills. It also makes a loud vrooooom sound. The dial to the left of the speedometer (I think it's the RPM?) goes all the way to the right, but the car isn't moving. It usually happens for a couple seconds, then I'm able to accelerate out of it. A few mechanics have looked at it and claim nothing is wrong with it. One mechanic checked the transmission fluid and said there is enough fluid, but that it's dirty and that may be causing the problem. I'm not convinced that would cause this.
This sounds like a bad transmission. There are a few things that can cause this in an automatic transmission (though I hate them and stick with manuals, so I'm no pro on the auto trans):