In preparation for what I think is going to be the most common question from Window Mobile users coming over to Android.
This was the first thing I
goggled 
MercuryStar sums it up nicely at
xda
'I'll attempt to sum it up once and for all, to try and set the record straight.
In Android's virtual machine, there is no functional differentiation between "closing" an app and "switching away from" an app. They are the same (the exception is things like music players which need to keep playing after you switch away from them, but even then only the 'service' part needs to keep running).
Whenever you switch away from an app, its current state is remembered so that even if it is effectively "killed" it can be returned to in just that state next time it's opened. Then Android either kills the process or it keeps it open, killing it when it needs the memory. You won't notice any difference between either scenario, except maybe that an app loads a little bit faster if it was kept in memory. At any rate, "closed" apps do not "run", and they do not take RAM or CPU cycles from other apps.
In terms of process/memory management, Android's VM has more in common with a web browser than a desktop OS - sure it can remember your state when you switch apps (like switching tabs, going back/forward/home in a browser) but whether behind the scenes it loads it all into and out of memory when you switch back and forth, or it all stays in memory is irrelevant to the user. Nobody worries that a long forum page on another tab or in their back button history is occupying 80 megs in the background or not, the browser takes care of loading/unloading it from RAM as needed, and that's just like how Android's VM works when switching between various pages of various apps.
Once you understand this you understand that all these 'task killer' apps are really unnecessary - all they'll do is make it slower to restart an app once closed. They don't reclaim RAM that was previously unavailable to other apps.
To cut a long story short, pressing "home" is a great way to close an app, whether you want to return to it later or not.'
developer.android.com Explains it in depth.
But as a former WM user I'm still picky about what's running in the background and because I occasionally catch sprint bloat running.
Here are some task managers
(Cyrket links, but they are all in the app store)
EStrongs Task Manager
Also Pressing and holding the HOME button is just a list of your last used apps, it isn't a task manager.
Hope this helps or saves from a 100 threads opening. Feel free to add.
At the end of the day we all WM users and that methodical need to check what is running is going to take some time to get over.