From memory (not that tough a task, I was present for most of these):
1979 - Spectacular Bid, 3rd - He got a safety pin caught in his hoof the morning of the Belmont, plus his jockey moved him to challenge a hopeless longshot early. Probably the best horse to win the first two and lose the Belmont; he won all 9 races the following year and set several track records in doing so.
1981 - Pleasant Colony, 3rd - Improved a ton in the race before the Derby and appeared to be knocked out by the 3 huge efforts going into the Belmont.
1987 - Alysheba, 4th - Uncharacteristically showed speed and tired; the winner had finished a close 2nd in the first two legs so wasn’t a surprise; another horse who was dominant the next year.
1989 - Sunday Silence, 2nd - Had equally-talented archrival, Easy Goer, who loved racing at Belmont and ran the second-fastest Belmont ever that day. Had either of these two horses not had to face each other, they probably would have both won Triple Crowns.
1997- Silver Charm, 2nd - Happened to win the first two legs against a couple of closely matched rivals, and just got run down late by one of them here.
1998 - Real Quiet, 2nd - Just got beaten a nose by equally-talented rival who had finished second in the first two legs after opening up a lead coming out of the turn. By the way, if California Chrome loses tomorrow, I think this is the most likely scenario.
1999 - Charismatic, 3rd - Like Pleasant Colony, improved a ton 1 race before the Derby, and was overused in his 3 straight big efforts. Broke a leg very late in the race; finished anyway but was saved when his jockey jumped off just past the finish.
2002 - War Emblem, 8th? - Pure frontrunner who stumbled out of the gate and was immediately taken out of his game. There are quite a few horses with a front-running running style who quit when unable to reach the lead.
2003 - Funny Cide, 3rd - Was too keen for the race; had a very fast workout that week and tried to lead all the way; beaten by talented rivals, including the Derby favorite who had finished 2nd in that race.
2004 - Smarty Jones, 2nd - Beaten by race tactics. Hounded by two rivals in the early portions of the race and ran way too fast in the middle part of the race as a result; still opened a lead coming out of the turn but couldn’t hold off a fresh challenger who had stayed out of the early fray.
2008 - Big Brown, eased out of the race - Who knows? Take your pick of a) loosened a shoe on the first turn; b) went nuts in the “detention barn” where stakes horses must wait during the day while they are watched; or c) did not receive his monthly dose of (then-legal) steroids for the first time.
2012 - I’ll Have Another, scratched - Scratched the day before the Belmont (and retired) with a flareup of a chronic leg injury.