GMail is the ultimate email client. Humorously, the capabilities that are so great for email actually enable several other "features".
1) Note taking - Any time I think of something interesting that I may want to remember, I write myself an email with the subject starting with "howto:". A couple that I visit often are "howto: make SEO work", "howto: deal with meetings" and "howto: amuse users while they are waiting"
2) Bookmarks - I never could get into sites like del.icio.us. Something about going to another site to create a bookmark just didn't make sense. I tried to use the bookmarklets and the browser plugins, but nothing made sense. Then one day I searched for a note that I knew had a link in it because I wanted to find the link. That was when I started sending emails to myself with keywords in the email to help find the link.
3) To do's - To do's are just short lived notes. I almost always delete them after they have been completed. For some reason actual to do lists or to do list software (web based or fat client) just doesn't work for me. I have started to believe that I have to-do-list-ophobia. But if I send myself an email then I am impacting my zero inbox beliefs so getting that to-do email out of my inbox is a priority. Also, I am always checking my email so the to-do is always available, whereas if the to-do list is in software, I have to actively go looking for it. To-do's even have their own tag with the most annoying color combination.
4) File transfer - I can't count the number of times I have used GMail to transfer files from one computer to another. I have emailed songs, books and of course word documents. This "feature" may seem weak, but I would argue it is so strong that you don't even know it is is a feature. You just expect email to send files. Heck, when Gmail came out one of the first things people tried to do with it was put a file system on top of it. Of course everyone is using dropbox for this now, but I still use GMail from time to time.
5) Tell me about your alternate uses for GMail!