I've only ever done this with WA1 and its remake, since there's a pretty great piece that only plays on the title screen in both versions. It helps that if you dwell on the title screen, a secret cutscene starts to play. Disappointingly both versions of the game have pretty short themes that play on the title screen though. About 30 seconds in the original and 50 in the remake.

Ocarina of Time's title screen is what first comes to mind. The calming melody by itself is fantastic, but that combined with the scenery of Link making his way across Hyrule really evokes a special feeling. https://www.youtube.com/watch?v=g2wzMZzdNJA

I've got a habit of letting Twilight Princess' title screen on for a little while because it's just so awesome. I also do that with New Vegas sometimes to get myself in the mood for Post-Apocalyptic wandering.

I don't usually let it sit, but I've always liked Pokémon Platinum's title screen. Something about a glowy dragon Satan was always cool to me. http://pa1.narvii.com/5741/aad2c5c8876fb70ee8e43f02dadf309de3054301_00.gif

Bulletstorm's title theme is the shit https://www.youtube.com/watch?v=MBN-d5Drp7U

I used to do that with KH2, because Dearly beloved is beautiful. As soon as i started the game on PS2 i would just stay there for a bit. https://youtu.be/IM-r2hxtO8g