While thinking about how to tackle my backlog of games, I though I might just give each game some said amount of time, around an hour perhaps, and then decide if the game is worth playing based on that. The problem is that some games might have a very slow or unrepresentative beginning but really open up later on. 

What are some great games with poor/slow openings?

Do you ever stop playing games if you don't enjoy them early on?

Do you think you can accurately judge a game based on the first hour or two?

Wolfenstein: The New Order. Glad I kept playing after the prologue. Its a great game, but the beginning was rather boring.

I hear Ocarina of Time is slow to start, but has a great pay-off.

I don't know about that, because all I've played is the first third...

FF7 - I had no idea what the hell was going on. I was so tempted to quit and never return until one of my friends told me, once you get out of Midgar the game lifts. Damn he was right.

Hybrid Heaven - Same as FF7, had no idea what was going on and the games story took so long to tell to make you understand. Great game and i am so glad i finished it. Underated gem on the N64.

To me, the game that can finish on a high is better than a game that starts high and drops the ball at the end. Something about good endings make me remember the games more. The two games above are perfect examples poor/slow starts but finish on a high and i place them in my top games that generation.

Twilight Princess, Skyward Sword, and Pokemon Sun/Moon, altho some people may argue against Skyward Sword on the "Great Game" department.

Every Final Fantasy game ever is like that, more or less.

Skyward Sword and Twilight Princess start slow but I find their context building quite nice so I don't mind that much.

To give an unconventional answer, most Total War games, especially Medieval 2 and Rome. They are fantastic games, with Medieval being the peak of its franchise and a highlight of the RTS genre. But the start of campaigns in those games can be very slow. But if you stick to it, the game gets better and better as your empire expands and wealth grows. Third Age Total War is another one. Yeah, it's a fanmade total conversion mod but it's practically a new game and is fantastic but again, slow start.

Twilight Princess and Skyward Sword

I hear people say Persona 4 takes a bit to get going, but I enjoyed the opening enough not to mind.

Most of the 3D Zeldas like to take their time to get the story moving, with the exception of Majora's Mask.

It took me months to get past the first few hours of Chrono Trigger...and then a few weeks after to finish. I can't remember if that was just me though...I get distracted a lot.

I can attest to that with Chrono Trigger.  It's actually a good red herring.  You think "oh boy, here's another save the princess story" and then after saving her...you get arrested and it all starts to get a lot more interesting :P