To add a little more than just another vote for Thunderbird....
I recommend using Thunderbird (if you must use a desktop client) using IMAP to link to your Gmail account. Google "thunderbird imap gmail" and you should find something to get you started. But basically IMAP allows you to sync your local email with the email on the server, unlike POP3 which just does a straight download and allows you to either keep the original on the server or not - there is no "synching" so to speak. So you can manage your email on your desktop pc and still have the same email structure when you log in to your gmail account through any web interface wherever you might happen to be in the world.
Honestly tho, I'd just suggest use gmail's web interface in your browser. I used to strictly be a Thunderbird supporter. But gmail is perfect. I don't have to worry about backups. And I have it where ever I go. And the serach feature is great. If you use Firefox, there are some good extensions out there. I like "Gmail Manager" extension. The ability to use multiple accounts and multiple identities is great for me. I have a ton of email addresses, and I can check them all from one account. Also, I can send email as if it were from any of those email addresses from my one primary account (ala multiple identities).
I just value portability over the benefits of a desktop email client. I challenge anyone to point out a feature found in TB that is not found in Gmail's web interface. I'm not saying there isn't one, I'm just saying I haven't found it yet.