Good advice from Wayrad, although thought I would add to it. It's not that it's running that drains you like he said, it's if it's using CPU cycles (that's what burns battery or slows you down).
A great application for this (Rathe than a task killer) is "Watchdog" instead of just shutting down apps for no reason to open memory you don't need:
Instead, what it does it watch all the apps in memory and sees what is using CPU cycles. Now if an app is poorly coded and is acting badly, it may outta no where start to run the cpu for no reason, WatchDog would see this and shut it down.
So basically instead of shutting down for no reason, it will shut stuff down but only if your not using it and it keeps tapping your cpu. You can set the polling rate (how often, and the CPU threshold, just use the defaults, you'll be fine.
Also, as a nice thing, it also allows a 'widget' where you have a little screen showing %active CPU %Idle and how many apps are currently in the mem.
Anyway, prior, I always used Advanced Task Killer,till I really understood how it uses memory and likes to fill, etc.
I had the PC in mind, where even if an app takes 10Meg to run, then it mght use all kinds of extra memory when running, not the same on the Android. if it says it takes X Meg or KB or whatever, then that's what it needs and puts it in memory for when your ready for it. If the mem fills, or it needs extra it will automatically close down base on your usage. Better to not use the task killer.
Check out WatchDog.....NO I have no affiliation to them, although after this post I should get a commission hugh( Actually it's free, I think the pay one has only 1 feature extra?, nothing big..)
Oh well..good luck...Jeff