Sorted them by platform. And I had to really dig through Wiki to identify oldest ones ^_^
ZX Spectrum Galaxians - my friend had Spectrum and that was my first introduction to computer games. I loved it for being a novelty, but as it always took us a long time to find right place on tape it didn't last long.
Elektronika MS-0511 - first 'real' computer, my best friend's school had computer class and they were allowed to come after school and play.
I can't find the game I was playing there, it was a kind of reverse from Galaxians - you were flying over a 'city' and had to shoot off the tops before you crashed in them. Once again was a novelty-fun but as those computers tended to have problems and crash every now and then, it also become a reason I was afraid of using computers, being sure I will break something.
Dendy and 'Super Mario Bros.' were my first addiction. Dendy didn't allow to save progress, but the game itself was on a "100-in-1" cartridge, and I could play any level I wanted. A threat of taking that cartridge away was a good motivation to get me to keep my marks up.
And as for PC... I don't really remember ^_^'. It was either some English-for-Children picture game, based on 'Arthur' animated series or 'DuckTales: The Quest for Gold'. I loved both and when I finally had my own computer I tried to find them - and failed. Original CD's my cousin had were long lost and they were too outdated and were no longer sold.