My most random encounters would have to be at the mall I work at.
One day I was working a fitting room shift and two people came wanting to try on footie pajamas. They might have looked semi-normal to other people but they couldn't fool me -- they were cosplaying Prussia and England from Hetalia. They were casual versions but as a Hetalia cosplayer myself at the time I could still tell totally what they were up to. Sadly I never worked up the courage to say anything to them.
Another time I spotted a Rin Kagamine cosplayer in line at the registers.
More recently, I was aimlessly wandering the mall before my shift and I spot a Dave Strider cosplayer walking with a Terezi cosplayer. I'm not a fan of the series at all but it made me pretty excited to see. My way of approaching them was weird, but I didn't have much time to think. We passed while walking opposite ways so I just said "Hey I like your Homestuck cosplays." and kept walking like a weirdo. They followed me though and we ended up chatting for a good 15 minutes! Turned out they actually remembered me from one of my cosplays from Anime Boston, yikes!