I don't use a desktop e-mail client at all. I simply always have the Web version of Gmail open as one of my browser tabs. This means none of my e-mail is stored locally. So far, that hasn't been a problem.
When Google announced offline access, I hesitated slightly due to the size of my in-box, but then realized 2.57 GB isn't all that much to download and store, especially if it means having access to vital data when I am offline (which, admittedly, is a rare thing).
Since both of my laptops have about 50 GB of free storage space available, I was happy to sync my e-mail and not care about how much space it takes up.
Many, however, may not be so carefree with their storage and e-mail archiving. If space is at a premium for you, consider Gmail's newest trick. You can now set the maximum attachment size to be downloaded for offline access. Sizes range from attachments of 10 KB to attachments of 10 MB. You also can set Gmail Offline so that it won't download attachments at all. If you're like me, you can ignore the limits altogether. Gmail currently allows for maximum attachment sizes of 20 MB.
So there you have it. You'll be able to control attachment sizes when your offline symbol reads "0.2" at the top of your inbox. This feature isn't supported in version 0.1.
