Microsoft Works has a standalone application that allows you to see reminders
even when the full client is not running or active (wkcalrem.exe).

Searching, I can't seem to find a free app or plugin that:
1) is free
2) can do this for Outlook for a Microsoft Exchange Server account (not POP3,
IMAP, or HTTP)
3) that I can install without administrative rights (basically anything that
lets me choose where I can install it, and doesn't write to the registry)

Why do I need this?  At work, I have two machines with a switch.  Since we
moved to Outlook from Lotus Notes, I miss meetings all the time, because I'm
working on the second machine that doesn't have Outlook.  I'm pretty sure
they'll reject my request to have Outlook installed on the second machine,
even though I used to have Lotus Notes on both machines.