Actually, thats pretty tough. I don't usually play to dickwave, but I'll usually end up with a respectable record overall if I actively try to improve. Got lots of 'worsts'- too many to count, but I'd say my best is a tossup between going on a hacker-hunting rampage on a Serious Sam server way back, ending the night with a KDR around... 632/136? Or the self-imposed Desert-Eagles-Only match I played in Combat Arms, scoring close to 130/30 by the end of the match.
Not exactly one moment in particular, but a few seasons back, I managed a 20 game deathless win streak in LoL. I really should have kept up practicing.
...Actually, now that I think of it, one of my worst has to be the ensuing days-long losing streak I went on immediately after. Literally the worst luck.