There are so many.
For the bad:
Probably all-time it would be the "Greatest Game Ever Played" -- the 1958 Championship Game vs. the Colts. It's the game that shot the NFL nation-wide and the Giants lost it in overtime (the only championship to end that way) on extremely bad referee calling. That was in the middle of a golden era where the Giants had Vince Lombardi and Tom Landry on the same staff, they went to championship games 6 times in 8 years (56, 58, 59, 61, 62, 63) and only won the 56 game.
In the modern era:
- 1978 "Miracle at the Meadowlands". Leading the Eagles and on course for the playoffs for the first time in 15 years, all they needed to do was hand off the ball and the game was over, victory in hand. Only the "Victory Formation" hadn't been invented yet. They hand off the ball to Larry Czonka, he fumbles, Eagles recover, win the game, Giants season torpedoed. However, this disaster was the catalyst that spurred the modern Giants -- after the season ended they brought in George Young as GM, he drafted Phil Simms, and brought in a new coaching staff that had Bill Parcells on it.
- 1985 - in the playoffs against the Bears they got DESTROYED, lowlight being the punter completely missing the ball in a kick and it's returned for a TD.
- 1988 - Jets knock 'em out of the playoffs
- 1989 - Lose in playoffs to an overtime stunner by Flipper Anderson on the first play
- 1993 - Playoff loss to 49ers. A last hurrah for Simms and LT, they went toe-to-toe with the Cowboys for the division in the last game of the season and lost. Cowboys got the bye and a home game, Giants had to play the 49ers on the road. Disastrous thumping and official end for two Giant greats.
- 1997 - Playoff loss to Vikes -- up by 9 points with 90 seconds left they lose the game and the team starts fighting with itself.
- 2000 - SB XXXV. After destroying the Vikes 41-0 in the NFC CG, they get destroyed by the Ravens 34-7. NOTHING goes right.
- 2003 - Playoff loss to 49ers. The "Trey Junkin" game. Giants up 24 points allow the 49ers to come back and are still in position to win the game at the end with a field goal. Snap is botched and the result is an incomplete pass but there was blatant holding downfield that should have given them another snap but the refs blew it, even got an official apology from the NFL for blowing the call. But the game still counted.
2005 - Home playoff loss to Panthers, 23-0. Complete no-show.
2008 - Home playoff loss to Eagles, 23-11. Complete no-show, blew #1 seed.
2009 - Last ever game at Giants Stadium. With the biggest assembly of Giants greats ever, and with playoffs on the line, you'd think they'd be motivated. Nope. 41-9 Panthers in another no-show.
2010 - Eagles game. Win this game and they lock up the division. Up by 21 points with 7:30 left and they lose the game. Onside kick, kick to Desean Jackson, game over. The following week against Green Bay playoffs are still on the line and it's another no-show.
I'm probably forgetting a few...