1. The first one I remember having at home was an IBM PCjr, bought by my dad for the family to use when I was in either middle or high school (hard to recall). He was working for IBM at the time, so he probably enjoyed the discount he got on the thing. I did get a decent introduction to BASIC programming with it, though. The only thing it was useful for otherwise was games (King's Quest seems to be a shared favorite between EJ and myself).
2. My first laptop (and second computer) was a Tandy 1100FD, bought on closeout while I was in college. This was used mostly for tinkering around and some of the assembly programming assignments I had. I also got my first taste of BBSes with that thing. It wasn't good for much else, not having a hard drive.
3. My first dedicated Linux machine (hobbes, and later camelot) was custom-built, starting with a K6-2/450 and 128 megs of memory, after I moved to the NC Triad area. It has since been rebuilt 3-4 times... the processor is still the same, I think, but it's up to a half gig of memory and a 90-gig RAID array for storage. It hosted my personal domain for a while, but now it's just the house's primary server.
4. To facilitate working from home, when I first started working in my current job, I built an NT 4.0 machine and installed what was necessary for that task. It has since been upgraded, both in hardware and the OS, and set up for both development and multimedia work. I haven't yet found a good use for the latter, though. That machine's name has always been mordred... anyone who knows my opinion of Microsoft should be able to figure that one out :-)
5. The second laptop was a cheap CompUSA-branded thing that got me by for a little while. I ended up selling that off to a friend, when I bought...
6. ...my current laptop, a Gateway Solo 5300. It still works rather well for me, esp. after upgrading to Win2K and putting a half gig of memory in it. It could probably use a hard drive upgrade, which I'm likely to do later.
I'm not sure if I'd include my new Linux server, excalibur, in this list or not. It's technically not a "personal computer", so to speak, and also isn't located at home, but it's pretty nice to have and is what's currently hosting my personal domain. If I were to include it, it would be at the end.