In my opinion, fights where you want both guys to win are the best. Even better than when you really want someone to lose. Anderson versus Chael was this way for me. I wanted Anderson to win, but I would have been by no means upset if Chael won.
Frankie versus Jose. Really wanted Frankie to win but happy for aldo.
Conner versus Aldo. I'm curious as to the outcomes proceding either fighters victory. I wish I could watch the press conferences for both men's victory.
Uriah versus Frankie.
Pettis versus Benson.
Others? 
Shogun Hendo
Recently it was Kelvin vs. Woodley 
Silva v Diaz.
Machida vs Weidman
Shinsei78 - Silva v Diaz.Ditto. Nick's the fucking man and you couldn't hate on Andy (until now...).
Silva vs Chael
Brown vs Lawler
Rich vs Chuck
Cain vs JDS
GSP vs NBK
The biggest was Rich vs Chuck broke my heart to watch my two favorites trying to kill each other.
Brown n Lawler
Rich n Forrest
Stann n Chael
Great thread OP. There are so many - that is one of the things I like most about this sport. You might root for a person based off of personality, technique, fighting style, or impact to a division. So often those conflict and we end up rooting for both. Some that come to mind:
Hendricks v Lawler 1
GSP v Penn
Edgar v Faber
Silva v Hendo
Silva v Chael
etc etc etc
Most recentl Gaetchje (sp?) Vs. Palomino...I didn't care who won coming in to the fight but during the fight was cheering for both guys
DC/Jon
Lauzon/Cheisa
Jojo/Rose
Frankie versus Maynard
Diaz versus Silva
Eddie vs Cowboy.
Was really happy and excited for Eddie getting his shot in the UFC, but Cowboy is one of my fav fighters so it was tough to pick sides
Gatti/Ward 1
kennyfrommd - Frankie versus MaynardShout out to all you Frankie fans. We've been through some tough shit.
Diaz versus Silva
Frankie/Maynard II was what sold me as a Frankie fan. Before that, I thought he was just another solid contender, but watching him stumble around the ring and struggle back to his feet time and time again made him look like Rocky. He forever earned my respect with his gameness in both of those fights.
Lawler Hendricks 1
I was just stoked for a new champ.
Wand vs Chuck