Is there a way to show usage stats for installed applications on my Android phone? I'd like to know how much I use my apps and if there are any I can get rid of (because I don't use them).
Try Spare Parts app from the Play Store (it's built into some older custom ROMs). Under the "Device info" heading there is "Usage statistics" which should give information you're looking for.
SystemPanel provides historic app usage statistics.
I also have developed an app called "App Usage Tracker". You can download it here from the market .
I developed a free app called "AppUsage". You can find it on Google Play.
The fact that an app is running doesn't mean you're using it.
Settings > About Phone > Battery Use will give you a run down of what has been using juice on your phone, a good clue to whether the app is doing anything. You can also run a task manager -- How To Geek suggests Advanced Task Cleaner. Both of these options will tell you what is running, not what isn't running, but you can extrapolate from there.