We use Gmail on several business accounts and forward mail between them for backup. We also use Thunderbird to download and backup all online accounts.
Keep in mind that on the free accounts there's zero tech support besides their forums - it can be unnerving when occasionally you can't get access to your account.
We've found one major bug: if you're having a dialogue with someone, and the messages string into a 'conversation', sometimes a new incoming mail is not shown 'unread' in bold. It can be a killer. One workaround is to change the subject line, even by a character, or space, when replying. It is the identical subject line which appears to group a dialogue into a conversation.
One other minor problem is that we can't test email forwarding on other webmail setups. Sending an email to yourself makes it back to your Gmail account but isn't accepted by the Gmail system (apologies - badly explained).