I think it depends on how much they pay for it. If the price is high, then they want the product. If the price is low, they want the people. Of course even if the price is high, sometimes companies muck it up anyway.

If the price is high they want the user base.

I don't think big companies care too much about a product in itself. They care about the team (which created a good product) and/or a userbase.

Good point - I hadn't considered the userbase. But don't they lose the userbase if they crap on the product after it's been acquired?

Absolutely. I consider that a failed acquisition -- which many companies do. Yahoo!, for example, had done this a lot in the past with their acquisitions.

The worst is they shut down the product and the team was assigned work in unrelated area. I would say most of the time these companies just want to control the future of the product, it's more a defensive act.