Normally I tell people not to use one if they ask. This is because if you don't know too much about how android works, then using a task killer will cause you problems, even problems you don't realise.
Having said that I use a task killer, but I ignore every single core service (everyone should do this), and I have about 20 other items on my ignore list.
You really need to be smart about it, and in my view should only be used to kill those 3rd party apps that do not correctly apply their services (there are a few developers that don't seem to understand the android os either..)
So in reply to this i'd go with no, you don't need it. There are apps running in the background but android itself can manage these. Try without and see for yourself