I'll be on a flight for a long time and need to respond to email.
I use a Mac and Gmail.
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The easiest way is to just set up IMAP in the GMail settings and then use your favorite desktop client. (I use Apple's Mail)
However there are some big gotchas with this method. For one if you poll GMail's IMAP server too often Google will think you're a spammer. At first you'll get weird “account exceeded bandwidth” errors when connecting. You can go to Google's page for proving your not a spammer to fix this (below)
Google advises setting your polling (how often you client checks for mail) to at least 15 minutes. I'd advise going to 30 to be safe.
Unfortunately most people who want IMAP do it to sync multiple systems for offline use. (Say an iPhone and iMac and potentially a desktop) There's basically no way to do this with GMail without running into these bandwidth issues. Eventually Google will just stop letting you log in even if you prove you are who you are via the above web page. Needless to say this makes using GMail via IMAP far, far less useful than it otherwise would be.
My workaround to this is an other solution to using GMail offline. Simply forward all your Gmail to an other account that has a more functional IMAP setting. You can do this in the settings in Gmail.
The simplest solution would be to use the official Google Gmail Offline Chrome Extension.
It lets you gather, say, the last 30 days of email in your Inbox and stores it offline for you wot work with in a simplified Gmail interface. Then, once you get back online, syncs up with Gmail again. I've used it and it works well.