Ever since I've had my first computer of my own, I've been using non-Microsoft software as much as I could, except for my OS. Many of my friends have given me good reasons for using alternatives ,and at first I did it just because they said so. Over time, I've grown used to it, and I've also learned more about the advantages, so that nowadays I'm often telling others why they should not use Outlook or Explorer.
So what do I use?
For e-mail, I've been using Eudora for many years. It's a good solid product with nice features. I've always been happy with it.
My browser is K-Meleon, which has grown into a mature browser while I was using it. It used to have an unfinished feel about it but lately it's been getting really good.
Before that, in days of old, I used the Netscape Communicator suite. And I may well be going back to it now.

You see, the company that made Eudora has given up on it. They have handed the code over to the Open Source community, which is in itself most commendable, and I wish software companies would do that all the time with software they'd stop developing.
Currently, an open source version of Eudora is being developed under the name of Penelope. But it's taking them a while, and I'm not sure I want to wait that long. Of course, I could continue using Eudora even when it's not being updated anymore. But wait...

I heard about another interesting open source project, another member of the Mozilla family: SeaMonkey. This is actually not one program but a suite, much like Netscape Communicator was: it contains a browser, an e-mail client, and a HTML editor. In fact, this is the successor of the Communicator suite.
I decided to take it for a spin today and I find myself liking it so much that I may ditch both Eudora and K-Meleon in favour of SeaMonkey.

The browser feels solid and fast; it runs on the same engine as FireFox does (as does K-meleon). My only gripe so far is that it doesn't let me grab and drag the toolbars to a new location. In K-Meleon, I can even stack them so the shorter ones can be in one line together. On a 12" laptop, screen estate is valuable!
But otherwise I felt right at home within the hour. (It may take you a little longer if you're coming from IE. But that's only fair since you have so much more to gain!)

The e-mail client looks slick and doesn't seem to be missing any features. It has a very nice search bar that will allow fast and easy searching for text in message subjects.
Furthermore, it imported my existing mail, server settings and address book from Eudora without batting a digital eyelid.

I'm impressed so far.
If you're looking for both a full-fledged browser and an E-mail client, I suggest you check out SeaMonkey.