I was 2 and a half or 3ish when my sister and I saw our first home computer. It was a 286 IBM Clone, with 2 entire megs of RAM and a 1 Gig harddrive, two floppies, a 5 1/4 and 3 1/2, and we even had Exmem, so we could use our whopping amount of RAM in DOS!
It ran at 16 mHz, with a Turbo mode of 33.
I remember a lot of DOSShell, and learning a few arcane terms-- such as TSR. I remember a few of our games would hog all the RAM for themselves, and we'd have to reboot to clear it out so we could do something else. What a pain in my side.
It got upgraded to a 386sx sometime later in its life, though I don't remember when, and we got something new-- a CD Rom Drive, with Win 3.1 installed ontop of it, and 4 Megs. We were spoiled. It received another upgrade, bringing it to 486 with a new motherboard, so we could get onto the Internet in 1994, with a 14.4 baud modem.
I loved that machine, and I'm still sad that it's long-since dead. Sure, it was affected by the Y2K bug, so every time I wanted to use dad's old starchart software on there, I'd have to reset the time myself. Infact, I played games on it well past the year 2000, too. We got into Shareware really early, so we had several entire CDs and floppies dedicated to freely available games.
We played a lot of SimEarth, Caesar II, Skifree, Rodent's Revenge, PF Magic's Catz and Dogz, Chip's Challenge, Jill of the Jungle and Crystal Caves on that machine. I have a fond memory for delving into the Shareware discs and seeing what was on there, too, so yay fond memories of Shareware.
And the many games and clones it introduced me to!
And yes, we did get a computer upgrade, in 1996. A Windows 95 with a Pentium 100 Chip, 128 megs of RAM, and a 30 gig harddisk. We were spoiled silly by my parents, I guess.
My parent's first home computers were a TI-99+ and an Apple //e, which is now in the possession of my sister and I. We played a lot of Atom 20, Oregon Trail (both versions), Lemonade Stand (like another poster above), Wilderness Campaign, and a few odd MECC games we got from our computer teacher in middle school after the school got rid of their Apple //'s.
We also Print Shop for the //e, until the disk corrupted itself one day. It was a blast.