One of the ways in which smartphones are different from PCs is that you usually never shut down an app on a smartphone. In most cases when you switch from one app to another on a smartphone, the app that you do not see is still running in the background on the phone. If you want to shut down apps that are running on an Android smartphone you can use one of several different task managers like Advanced Task Killer. If Android 2.x is on your phone you can tap Menu, Settings, Applications, Manage Applications and tap Running to see a list of the apps currently running; tap an app name and then tap Force Stop to shut down the app.
The primary reason why apps are not shut down on smartphones is that apps load much faster if they are already running than when they have to start up from scratch. Microsoft created this behavior in their original handheld operating system, Windows CE, which monitored memory and automatically shut down apps when the operating system needed more memory. Originally Windows CE was not aggressive enough in shutting down apps, so once too many apps were running the phone started to slow down. Developers created task manager apps so that users could see what apps were running on their phones and shut them down in order to keep the phone running as fast as possible. Over the years Windows CE and Windows Mobile got much better at automatically shutting down apps, but long time users had the habit of using task managers so they remained popular.
Android treats running apps the same way as Windows Mobile, once an app starts it is always running until Android shuts it down to free up memory. Task managers have also become popular on Android and you can find several of them in the Android Market. Lifehacker has an excellent article about task managers on Android and explains why they shouldn’t be used. The article points out that usually when an Android phone starts running slow it is due to the CPU being over utilized by a bad app and suggests using Watchdog, which monitors CPU utilization rather than memory utilization. If you have an Android phone and are interested in learning more to get the best performance out of your phone, I highly recommend Lifehacker’s article.