Doing anything with the memory/CPU will cause the batteries to discharge. Sitting idle and waiting for a call with the screen off takes a certain amount of battery. Doing
anything else will increase the draw.
Let's look at a very common background request, having an IM client running in the background so that if one of your friends sends you an IM message (even if the phone is in standby) it pops up and you start chatting with them. It not only takes the CPU/memory to maintain the client state, but you also throw in the overhead of managing the internet calls necessary to report in. It has to look up the IM servers in DNS, ping them periodically, switch back and forth between 3G and wifi depending on where you are, etc. That's a lot of processing going on for not much activity. Multiply that times three or four apps and it'll start using quite a few resources. Plus, you have no control over what the app does. If somebody wrote a client that actually
crunched data of some sort the battery would drain very quickly. Savvy users would know why but your average consumer would not.