Manic Miner on the ZX Spectrum 48k, I think it was Christmas 1982... I was only about 5, and it took me ages to get past the 'Central Cavern' but I was hooked. It was a brilliant game then, and is a brilliant game now - and was also one of the first games to feature background music, certainly it was the first on the spectrum. The way it was done was the processor switched from playing the game to the music every cycle - which is why you got that wierd warbly effect on the music.
You'd never believe such a thing was ever a problem given the power of todays machines.