How much memory should a typical android application use?

You can use DDMS > Allocation Tracker to track memory usage and Heap Allocation for your app

http://developer.android.com/resources/articles/track-mem.html

To Track the overall memory of a PID you could use following two methods in ActivityManager

To get a PID of your app :

List<ActivityManager.RunningAppProcessInfo> getRunningAppProcesses ()

and then the MemoryInfo

MemoryInfo[] getProcessMemoryInfo (int[] pids)

you might want to take a look at this one. How do I discover memory usage of my application in Android? Or simply try

ActivityManager.getMemoryInfo() 

Android apps are constrained to a certain amount of memory. As it's quite (insanely?) low, I think you shouldn't feel guilty about using all of it!

The limit is 16 MB on very old devices, 24 MB or 32 MB on newer ones. There doesn't seem to be much info on the size for different devices, and nobody seems to know why the limit is so small when modern phones have 1-2 GB of RAM.

http://blog.javia.org/how-to-work-around-androids-24-mb-memory-limit/

https://groups.google.com/forum/?fromgroups=#!topic/android-platform/7zKQlrDcypQ

Aha, I found some concrete numbers on the limit:

http://dubroy.com/memory_management_for_android_apps.pdf

G1: 16MB

Droid: 24MB

Nexus One: 32MB

Xoom: 48MB