I was wondering if there was ever an event like the medieval crusades in Tamriel and who took part.

No.

Probably the only thing I can think of closest to that was the War of the First Council.

It was a Holy war?

http://www.imperial-library.info/mwbooks/war_firstcouncil.shtml. While is does seem to have a religious grounds to it, I'd not say that it was like the Crusades. It looks more like a religion based excuse to war with other Houses was used to, well, war with other Houses.

Don't forget that jerk Pelinal Whitestrake killing all those poor defenseless Khajiit just for the lulz.

The Dragon Break? lawl

I'd say no, because that was a rebellion. It just so happened that Pelinal looked like a crusader and at times would indiscriminately destroy things, remove places from the map, and kill anything that looked like elves. To be honest, his only crime was accidentally killing a few humans here and there when he went insane.

Right now, I can't think of a war that was started like the Crusades or the justification. Even the War of the First Council just isn't that close. That war was started because the Dwemer were making a giant stompy robot, and no one really liked that...Most of the wars are either fought because the nords don't like elves (perfectly justified), kingdoms trying to defeat each other for land and power, rebellions, or to take over Tamriel.

Closed: religious controversy. We are not going to discuss events on Tamriel in terms of a real-world religious war.