Do I really need to install a task manager?
Should I run a task killer on Android or does Android manage applications well enough on its own?
Android is very good at managing its memory such that task killers should not be necessary. Processes that are not on the screen will use essentially 0% CPU power until they are either re-activated, or have to perform some background work (such as downloading emails).
If you open so many programs that there is not enough memory left, the Android system will start killing off unused programs on your behalf. It is completely self-managing.
The performance of the phone should not be affected by the number of applications running. That said, I do keep one installed, because every now and again, a process can "go rogue" and start using a lot of CPU power and thus give poor battery life (this is rare though).
More background here: http://geekfor.me/faq/you-shouldnt-be-using-a-task-killer-with-android/
I agree with the general position that they are unnecessary, however I have recently come to the conclusion, based on personal experience that it depends which version of Android you are running. Let me explain...
I used to use a Task Killer on my Droid but stopped after I started seeing more and more people explaining why they don't actually work (see the links Al posted above). After I stopped using it I actually noticed better performance. I was baffled about how I used to think that using the Task Killer improved my performance.
Then I got a tablet running Android 2.1. This tablet has a faster processor than my Droid and more on board memory so logically it should perform better, however after loading a modest amount of apps it was very, very laggy. Out of frustration I turned back to my old fiend Advanced Task Killer and the tablets performance improved dramatically.
Trying to reconcile the inconsistent experiences I realized that ATK worked great on my Droid when it was running on Android 2.1. It was after upgrading to 2.2 that I stopped using it and I never made the connection that Froyo made the task killer unnecessary.
The conventional wisdom is still that Task Killers are unnecessary (even counterproductive) and for devices running Android 2.2 I wholeheartedly agree. For devices running 2.1 or lower, while theoretically they don't need them, it has been my experience that task killer vastly improves the performance of these devices (at least on the devices I used: Moto Droid and Archos 70IT).
In my own experience using a task killer can help your battery if you opened too much applications or you don't need them anymore like the facebook app running in background when you turned off wifi or the data connection (3G/EDGE/GPRS/whatever)