Are there any tools to analyze the usage of an Exchange mailbox

I'm not aware of any off-the-shelf program that does what you're talking about. You could script various data gathering mechaisms and report on that data however you see fit, but you're talking about a fairly "custom" solution.

1. You could get this from "Message Tracking" logs. The logfiles are ASCII text, and the various event ids are listed here: http://support.microsoft.com/kb/821905 I generally run w/ "Message Tracking" enabled in all my production installs, anyway, just because it's too handy not to have enabled. You do take a slight performance hit with it enabled, but I think it's more than worth it.

2. This could be scripted. You'd need to run the script as a user that has rights to open every user mailbox. (You could remove the annoying "Deny - Receive As" ACEs placed at the root of the organization, but be aware that service packs and updates could restore them. I always remove these annoying ACEs anyway-- an "Administrator" should be able to open any mailbox.) This would kinda be a fun script to write, but I don't have time today. Users could create server-side rules that would divert unread messages into other folders, so this might not give you an accurate metric.

3. You're going to have to parse the security log on the Exchange Server computer(s) for that. If you want to ignore the "logons" from Backup Exec you'll need to do that there, too. (Why is Backup Exec "logging-on", anyway? Are you doing a "brick level" backup? Ick... I avoid those at all costs. If I need to restore an item in E2K8, I just restore a database page-level backup to an RSG.) The "last logon" attribute that the Information Store maintains is single-valued, so the only other way to get this, aside from parsing the security log, would be to "poll" that value. That would be highly inefficient.

If you haven't thought about it, I'd track mailbox size and number of items (to compute average size per item). I've caught "abuse" of "precious" Exchange IS space this way in the past. Now that E2K3 Standard has a 72GB store limit that's not such a big issue. Even so, it can tell you things about your users usage patterns.

Sounds like this would be a fun system to put together!

Disk quotas.

Exchange Management Console > Server Configuration > Mailbox. Look for the Mail Store to manage, right click, go to Properties and set the limit there under Limits.