Any battle we don't get to see finished due to either someone interrupting or something big going down (like a Pokemon attack or something). And in other cases because it is not seen onscreen.
For me recent battles like Quilava vs. Pikachu stopped by Cynthia or Dragonite vs. Charizard being "N-terrupted" by N for some Pokemon/Trainer love crap.
Another one is Ash vs. Eugine (can't spell his name) the guy who is obsessed over Suicune. He was literally being a dick because he doesn't think Ash is worthy or seeing Suicune and calling him a liar. The battle was called off before it began due to the Bug Pokemon attacking the city.
Zoey vs. Candice after leaving the Battle Pyramid after Paul lost to Brandon. I wanted to see Contest vs. Gym Battle trainers going at it!
-Nando vs. Zoey in the Double Battle Contest round of the Hearthome Contest when Zoey lost and I was glad because she was bitching at Nando for doing gym and contest battles
-Paul vs. Reggie, he told Paul's Pokemon that he and his little bro would battle after he got back from the league after Paul had lost to Ash
-Tobias vs the Sinnoh E4 and Cynthia
-Dawn in the Johto Wallace Cup
-May in the Johto Grand Festival
-Pikachu vs. Brock's Vulpix in the giant Gengar, Alakazam and Jigglypuff episode from Kanto
-Virgil vs. Cameron, I seriously wanted to see Cameron go down in flames (well we did see Lucario get taken out by Fire Blast) after what he did to Ash!
-Any of the unseen battles from Ash in leagues that got skipped over or we only see the last round of that battle
-Paul's league battles from previous regions before Sinnoh or the matches that he swept through before facing Ash due to him not losing ONE Pokemon!
-Paul's rematch with Brandon
What about you?