I didn't make it all the way through all that many games, but there were one or two I managed it with. The one I remember most vividly was the wretched Captain Planet game that came in the Cartoon Classics pack. That took some serious doing, but I eventually managed it.
I'm fairly certain I made it through Paradroid '90. I was pretty hot at the original C=64 Paradroid, but I don't think that actually could be 'completed' in any meaningful way, you just had to do it over and over.
The Addams Family was great fun. I've completed that two or three times over the years. One or two bits of it were mind-bendingly frustrating, but otherwise I really enjoyed that game.
As far as I'm concerned, I've 'completed' The Settlers and Frontier. Neither really has a win condition, but I've survived long enough in both games to have pretty much done everything worthwhile there is to do.
There are probably one or two others. I might've completed Zool, but I can't really remember.
However, despite huge amounts of effort, Xenon II just never happened. I once made it to the start of level 3...