I currently use gmail, but this question is valid for any client: What is the best way to backup and store my email so that in the future I will be able to access it on a variety of platforms and clients.
Update:
While using gmail is certainly cross-platform and they have their own backup system, I am still looking to backup my email myself so that I can definitely know I have control over the backup and storage. I'm fine with letting gmail do it for now, but there's no guarantees.