It depends by what you mean by "significant."
Do you mean personal sense of accomplishment?
Do you mean social significant with my friends?
Do you mean a difficult "achievement" to get?
I have like a 4th world record for score on Crazy Taxi on Dreamcast, and that was pretty hard to do, as was S(at least)-rank all of Ikaruga (especially chapter 4). I found those both difficult to do.
Personal sense of accomplishment must be the fact that I completed all 111 levels of Supaplex sometime a couple years ago. My dad got me the game when I was 6, and, playing it on and off for 10 years, my brain finally got in shape to figure out and finish every challenge. I find that to be a goal I'm glad I met.
Socially, I won't really list my Online accomplishments since their meaning depends on what game my friends were playing at the moment, but I recently passed through the fire and flames at a friend's house. Which is funny, because I don't even have the game, and I know people can FC it, but I'd like to think just being able to pass it is a good thing. So some people are impressed and proud of me about that, along with my 5 star on Cult of Personality (I love the song...^^)