This is why I seldom start new games outside of weekends - Then, it is a nuisance if it takes 30-60 minutes to really "get going", but I can bring up the patience without thinking "Oh, come on, I really don't have all day..." since... yeah, I usually really don't have all day and it sucks if the intro and tutorial take more time than I have on a day

Wished games would put tutorials seperately or offer a pro-mode like "played a game of the series/a few games in the genre before"...
Nevertheless, yes, I agree with many in this thread, Persona 4 has a slow start. But it's so worth the wait and being a fan of Visual Novel-style games, I did not take too much offence. Zelda: Skyward Sword was a drag the fist hour or so as well and really becomes great afterwards.
Now for some games other than Persona, Yakuza and Zelda...
Ys Seven.
This is a game series all about running fast through dungeons killing dozens of monsters in seconds and fighting boss enemies which really test your reflexes all while eargasmic Synthrock motivates you to just play a bit more... It was a bit strange to have it start with about 30-60 minutes of introduction and talking to people in the city before killing your first monsters. Sufficient to say, later city visits were much shorter and the game rocks in almost every other way (I even liked the backtracking).
Trails in the Sky
This is also by Falcom. The game actually is about talking to people in the cities because the world and characters are really atmospheric - so slow pace is anticipated. But the first few hours feel like they start a bit too slow. Then, when the characters grow on you and the story picks up a bit, it's fantastic.
I really didn't want to pick on Falcom here, they produce some of my current favorite games. But I'm a big fan of in medias res-beginnings and I believe the beginning and the end of a game should be absolute highlights. The former to draw you in at once, the latter to make you want to replay the game again. (I also think Bayonetta had one of the best in medias res-beginnings ever

)