Many organizations utilize Microsoft Exchange for their email. I find exchange to be a very poor system, and do not like the typical methods of reading email on an Exchange server: Outlook or the Outlook Web App. I much prefer Gmail and Google apps for business. Specifically, I find that Gmail has superior search results, filtering capabilities, and a much cleaner look -- just try to stay focused while the email you're reading is surrounded by all of Outlook's nonsense buttons.
Forwarding or redirecting all email from an Exchange system to your Gmail account is often either against your organization's policies, or simply broken with no one willing to fix it. I wish it were as easy as setting an inbox rule in the Outlook Web App. This Instructables documents how I use Gmail and Google apps to access Exchange email. It's a hack, but it works.
For all the IT "professionals" and legal teams who somehow found this: Spare us your horror stories about how reading Exchange email on Gmail also sends a copy to the Chinese government (or whomever). There are good organizations that have made poor choices with regards to their email systems. Good people often want to be a part of these good organizations, and you need to realize that losing these good people by forcing them to use crappy tools is a far worse result than the Chinese government getting a few emails. Since subtlety isn't the strong suit of IT or legal, if everyone in your organization is happy using Outlook, there's probably no email being written that's even of interest to the Chinese government (or anyone else).
If you don't need the details (and don't need my further editorializing!), set Outlook to access both your Exchange and Gmail accounts, then set a local Exchange rule that moves email from Exchange to Gmail.
Step 1: Setup Outlook
I use OSX on a Mac. This should work on a PC, but your menus will probably be slightly different.
Go right into the belly of the beast and setup Outlook on your local machine. If your organization uses Exchange, you likely have access to a free copy of Outlook.
Setup your Exchange account. Next, setup your Gmail or Google apps account using IMAP on Outlook. If your Gmail account is large, this step may take quite some time. Further adding to the frustration, Outlook 2011 on the Mac doesn't give you an indication of what it's actually doing, so it will just be unresponsive as it accesses your Gmail account -- probably best to setup your Gmail account and go to sleep, it will be ready in the morning. You may need to enable IMAP on your Gmail account.