I use Thunderbird, which is the most full-featured of the three or so desktop email clients for Linux. Thunderbird aggregates my many email addresses in one place and allows me to manage my email mostly in the way I would like.
My biggest problem with Thunderbird is simply that it is not a joy to use. As a tool, it accomplishes the job. Maybe that's all I can expect.
It seems like many people are releasing very cool webmail solutions. But webmail is kind of gross. I have yet to find one that does a great job aggregating several accounts in a seamless way. It requires my webserver to be able to see the folder where I store my mail, which is a big concern (or alternately it requires me to run an intranet-only webserver for the explicit purpose of providing webmail, at which point why not just run a desktop client?). And I am extremely skeptical of any end-to-end encryption strategy using webmail...I understand that an HTTPS connection to the server + secure encryption on the server before transmitting should be sufficient, but it doesn't feel right. I'll be over here in my tinfoil hat if you need me.
Writing a desktop email client for Linux is not the way to get massive loads of HN karma. It's kind of unsexy, and since in the Year of our Lord 2013 it is still unnecessarily difficult to write something that looks nice and runs on multiple platforms, only a few die-hard throwbacks will be grateful (and half of them are running mutt or pine anyway and will sneer at your sissy X windowing system).
OK, so I probably answered the question I opened this comment with, but it was rhetorical anyway.