There was an online game I used to play as a kid called Bouldermania. I remember liking it, though it's been ages since I played it. It doesn't seem to be available anymore (though I'm pretty sure there are similar games with slight differences). All I can find now is this tiny screenshot – somehow I remember it looking a lot better than that.
I also remember a few other online games over the years that are no longer available, such as Big Fat Awesome House Party (a Foster's Home for Imaginary Friends game) and a Moomin fishing game, but this one is especially nostalgic, as it might have been the first game I played online after we got a computer (before I really got into gaming in general).
Probably not the best games there are, but these are the ones that are genuinely lost to me – I have a lot of games I haven't played in years, but for most, I still have the cartridges/discs and the system I played them on, so I could get back to them if I really wanted to...