Currently playing Dragon Quest 8... very slow start haha. Already in 7 hours and just got past the first real "dungeon". It's not really a dungeon per se but kind of.

Persona 4 is basically a visual novel during its first 3-4 hours, after that it's damn good. A shame so many people won't give it a chance, well I guess if you don't enjoy reading too much text it will bore you anyways, since battles are probably 1/3 of the game at most.

Other than that, Kingdom Hearts II really has to be mentioned, especially if you didn't play chain of memories & 358/2 days beforehand (me as a kid lol). You have to swallow quite a few hours thinking who tf are Roxas, Namine, Axel, etc and why are Sora & co asleep. The beginning is so boring if you have played the game and already know the full story, thankfully the game picks up when you can use Sora again.

I hear Vanquish is good but I have no idea. I quit playing at the tutorial.

FFXII, normally I am fine with slow beginnings for JRPGs. But I had to do the first 12 hours 4 times before getting past it.

1st time: Played at Uncles
2nd time: Played at friends house when I was bored.
3rd time: Bought game myself and played on BC PS3
4th time: PS3 broke had to play again on PS2.

Well worth it though.

From a gameplay perspective, The Last of Us is incredibly slow. It takes a considerable chunk until you can finally start doing things. 

DQ7, Chrono Trigger, FF7, Pokemon S/M to name a few

Tried 7, yet? If you think 8 is slow... oh boy, 7 is much much MUCH slower XD

Gravity Rush 2 is thé most perfect example for récent games

I've heard a few people say that, and I don't get it. Within the first 10-20 minutes, you're in the first dungeon. How is that slow, especially compared to Twilight Princess and Skyward Sword? Their slow starts is why I keep putting off replaying them.

See I don't think OoT has a slow start.  I think it has a weak start from a writing perspective as there's no world or character building whatsoever (barring the one bit of somewhat interesting exposition about the Triforce) but that's par for the course for OoT :P.  Give me an opening that establishes characters and setting and why I should care over one that leaves the "reason I should care" to my immagination any day. 

But I can also see OoT being viewed as "slow".  Yeah you get to gameplay fast but the game doesn't seem to start to have much gravity to it until a bit further in.