I think the early ones for me would of been Manic Minor or Jetpac on the ZX Spectrum 48k.
The most important system that had impact on me though was the Amiga and there are too many games to list from here that influence me (not to mention demos, utils and cracktros).
Played Dune (Dune2 afaik, not sure) Civ, and XCom
on Amiga - Was there something better than that on Amiga?
Those were great but not as influential as those personal giants I mentioned,
Also some PS2 games was of some influence on my
experience (Tekken 5 , and Spartan, Total War)
Sadly I was playing wery little of both the machines,
both Amiga and PS2 were like jet of bright foam in quality.
Were there some machines with such excellency
in feeling and mood like some best of amiga or ps2?
Still I remember some clear dream feeling about some old simulator games on amiga (they probably was not so good,
(or maybe they was?) but remember the clarity and quality of the dream - which based on some glimpses in shops and magazine screenshots)
Some little games on Xbox360 and PS3 I know I do not like,
(thoug I know only a few), Some games on IPhone i know
(only a few too) I do not like too, (same with android,) and
Some on PSVita i know (also only a few) I do not like too.
The most modern game I got such dream filing on was Gothic3 on PC - that was quite dreamy good game too (I know only few modern games on PC, but at least there is one example of really enchanting game to me;
X360, PS3, Iphone, Android, PSVita - nothing worth mentioning I know )