Back in 1982, my first USCF rating was about 1600. One weekend I played in a tournament at the YMCA, and I beat a guy rated 1950. I couldn't believe it. I asked him, "Are you really rated 1950?" He said, "Not after this tournament..."
Have you ever won a player who was 200 points over you? I have!
2143 vs 2413! (1 min bullet, today)
Doesn't count much, because if you played a large number of games, you are expected to have something like these.
Very good games! Thanks you! 
I see @MainframeSupertasker!
Biggest win vs elo 1874.
once a 900 beat an IM rated about 2200.
Congrats!
Though, the only true time a person gets valid bragging rights is when they can beat Nakamura in a bullet match. 
I have played 4 grand masters--all in slow time limits and won from all 4. Not so unusual to beat higher rated players.
I beat fm 2300+ :pp
I've long lost the score, but I was around 1400 USCF and drew a game against a guy rated 1800. He wasn't too happy either.
That was in the early 90's, just about when digital clocks where available, but almost everybody still used analog clocks. Everything's changed since then, as far as the chess scene. Even someone rated 1300 USCF, nowadays, has more positional knowledge than back then.
Also, and I'd be embarrassed to do this nowadays, but back in the pre-digital clock days, it was a stratagy to try and complicate a game against a higher level opponent, just to make them burn their clock down. In the end, he wasn't in time trouble, but the complications did give me a dead drawn endgame.
But that's ancient history, especially with increment. Plus I'd say it's probably difficult to actually "complicate" a chess game in the modern era, just because of online chess, your very unlikely to come across an opponent that hasn't had ample opportunity to play complicated or messy board positions.
Some player thrive on complicated board positions, but it's not an attempt to win games as much as a preference to close the board up and not exchange pawns in the opening phase.
I mentioned on a different thread, that players gravitate toward certain openings and defenses in order to get to a middle game they're comfortable with.
Yes. I was 1276 and my opponent was 1589