Man, it's a beautiful, albeit lost art. Title screens were important for mood-setting, and I believe the Japanese really knew this. I read someplace about how certain temples require visitors to painstakingly hand-copy words or phrases before they enter, because this is (correctly) believed to put a person into a different state of mind, that they can actually properly appreciate the experience they are about to have.
Title screens from the golden era of gaming certainly seem to reflect this idea. The best of them try to tell you about the world you're about to enter, or just put you in the right frame of mind. So many beautiful examples here so far. So many wonderful memories.
I want to contribute!
Demon's Crest. If it isn't the best, it's pretty freaking close in my opinion. I don't think I need to waste words describing this one.
Evergrace. In my opinion, the game's kind of a dog. But man, I was not ready for the title theme's mood-setting energy. Really unique, and it's stuck with me for years.
I can't find footage of it, but Breakdown (Xbox) had a really cool menu. Everything about it, from how the title logo appeared, to the actual menu itself once you pressed start to enter it, was super slick and, for me, extremely memorable. As you went through the different settings, you were urged on by this driving, electronic beat in the background - which just perfectly faded to a moment of pitch-black silence when you hit New Game.