Do not expect an automatic, kill every app on the phone task killer. If you want that, this is not the app you're looking for.
Your phone is not that broken. The OS manages the apps running on it most of the time without a problem. You rarely should ever have to kill/restart an app! Android does that itself quite often. There is one hole though. If Android has no need to stop an app, that app can do whatever it wants. This is where Watchdog steps in. It will let you know when a background app loses control and exceeds your CPU thresholds.
Here is a good description of the android app lifecycle management.
The fact that you can see an application's process "running" does not mean the application is running or doing anything. It may simply be there because Android needed it at some point, and has decided that it would be best to keep it around in case it needs it again. Likewise, you may leave an application for a little bit and return to it from where you left off, and during that time Android may have needed to get rid of the process for other things.
A key to how Android handles applications in this way is that processes don't shut down cleanly. When the user leaves an application, its process is kept around in the background, allowing it to continue working (for example downloading web pages) if needed, and come immediately to the foreground if the user returns to it. If a device never runs out of memory, then Android will keep all of these processes around, truly leaving all applications "running" all of the time.
What Android doesn't do is alert on processes that aren't behaving well. They will eventually get killed if something needs the memory, but in the meantime, it can consume CPU and thus battery. Task killers address this in a heavy-handed way, and hurt Android's lifecycle management. They won't even work in Froyo due to changes in the API that prevent the kill feature.
If you've ever had your phone seem strangely warm or had a dead phone early in the day it was likely a runaway app on your phone. The CPU is a major consumer of the battery, so it makes sense to keep an eye on it. Watchdog monitors the phone's apps and alerts you when one is running in excess of your thresholds. The user can then kill, ignore, or
WhiteListthe application to optimize the phone's battery life.
When your phone seems sluggish or warm, you can now easily see what caused the problem.