vs Hulk Hogan, AJPW/WWF, 4/13/1990
This is everything you don't expect in a Hulk Hogan match. Exchanging of holds, stiff brawling, double juice, and a fucking good match. Hogan still wasn't exactly Daniel Bryan, but when he cared he could put on great matches like this. The story of this match is pretty much Hogan knowing he can't beat Hansen in an outright brawl, so he has to look for openings and try as many different things as possible just to survive. It all comes together really well.
The match was originally supposed to be Hogan vs Terry Gordy, until Hogan dropped the WWF title. Gordy, who had been fine losing clean to WWF champ Hogan but not coming off a loss non-champ Hogan, pulled out, forcing Giant Baba (AJPW's booker) to draft in Hansen on short notice.
vs Vader, WCW, 1991
This isn't the match with the eye incident, it's a short little brawl they had from Hansen's WCW run. Dusty and Ross really seem to be marking out at watching these two just slap the shit out of each other, which is really a big part of the appeal behind this match. As great as Japanese commentary is there's not much that beats Dusty and JR losing their minds at these two big men going all in with their strikes in a way you really didn't say in America at that time. I don't think Vader was Hansen's best opponent (That would be Funk, Colon, or Kobashi), but if you want to see a genuine hoss fest any of their matches is a good place to go!