System: Go to Settings\Apps. Then click any app – you can see the permissions
- Read/modify Gmail: Not sure which apps would legitimately require it
Android market: All app pages show permissions if accessed through browser. Else click download.
Permissions (free): Better UI, best when used in conjunction with Permissions Denied.
PDroid (XDA, Free, root required): Unfortunately does not work with Xoom, so I have not been able to test, but a good option for compatible systems.
Note: If you are really worried about privacy and data usage and have root, the best thing to do is to use a firewall. Everything else, including the above mentioned apps, should come second. I think Droidwall (free, root required) is the best app for this. Avast works, but I just found that (at least in EOS ICS 1.0) it switches off when Xoom goes to standby and apps can access the net (apps could access data in the background).
Hopefully this will give you some insight on app permissions in android and the tools to manage them effectively.