Here are some of the earliest games I ever played...
Miner 2049er - I believe this is the 1st game I ever played. Challenging platformer where you have to "paint" the ground by walking on every single square before you can clear the level. I think this game is what eventually fostered my love for platformers.
Lode Runner - Usually referred to as a platformer, even though you can't jump. Still a very nice game where you have to bury your enemies and collect all the gold. Or in the CGA version's case, are those dollar bills? I can't even tell...
Bouncing Babies - An unforgiving game about rescuing babies from a burning building. You have to move the trampoline to get them to the ambulance. I was never good at this game, but I remember watching my mom get to really high levels on this game.
Adventures in Math. Gotta bring in the educational games right? This helped out my early efforts in addition and subtraction. Pretty cool "dungeon romp" with the obligatory math component.
Alley Cat - Wow this game is cool. It is probably the most sophisticated game in the list in modern terms. Each of the windows you can go in has a different scene, all with different gameplay. There is one where you dive in a fishbowl, one where you have to steal food from sleeping dogs, ones where you have to steal some kind of icon, while a constantly cleaning broom is trying to get you, or spiders, or dogs, etc. Wildly varied gameplay and challenging to boot.. Alley cat is just a really neat game.
Well, there were some other games we had in those early days, but those were the most noteworthy. Some others that deserve honorable mentions: Zaxxon, Stargate, J-Bird (a clone of Q-bert, lol), Flightmare, Netherworld.
And who could forget Mavis Beacon Teaches Typing? :)