I'm actually surprised that I don't remember any turn-based elements from any of the many, many M*'s I played given the strong relation to traditional RPGs - the only big time-based event was when servers reset.

Archmage (magewars.com, probably the first really big browser game) was the first game I remember waiting for my next turn to be available on. Apparently there's a "reincarnation" of it running today. https://wiki.the-reincarnation.org/Archmage