I love a good main menu. They're a game's first impression and I don't think enough games put enough thought into how they should present theirs. Main menus are introductions to the world and characters, a window to peek into what you're about to immerse yourself in.
Dragon Age: Inquisition has, easily, one of my favourite main menus ever. First off, it is alive, it has a wonderful loop of Templars and Mages heading toward the peace talks at the Temple of Sacred Ashes, something which is happening as a direct consequence of Dragon Age II and is the beginning of this games events. It is directly linking to the games world and story. It has Trevor Morris' amazing main theme blaring, setting the tone perfectly and showing that Inquisition is moving away from the dark fantasy aesthetic of the last two games and is going to be an epic adventure. Additionally, the menu shows off in full force the beauty of the world and the Frostbite engine as Inquisition is the first Dragon Age game to use it, directly confronting any worry about lack lacklustre, which was a issue from Dragon Age II.
To put the cherry on top when you select new game the Temple of Sacred Ashes explodes in a massive surge of magical energy.
The temple exploding is the games inciting incident and having that happen as the player physically chooses to begin their story is genius. The anticipation this fills the player with, before the game has even begun, is like no other game. Skyrim for example, I think has a bad menu, it tells you nothing, relying entirely on the music to set any kind of tone.
Imagine if Skyrim had a similar approach to Inquisition, perhaps a shot of Imperial guards standing watch at the border between Cyrodiil and Skyrim, maybe a loop of people going through the border, then when new game is pressed Stormcloaks spring out of the trees and the Imperials ready themselves and sound the alarm. This would be a far more engaging opening, it could show off the border tensions, it introduces the Stormcloaks and sets up the carriage ride into Helgen.
It doesn't necessarily need to be all action or excitement either, The Witcher 3 has a menu I like too. It doesn't have any huge eye-catching action, but it is a perfect peek into the world and into Geralt, as well has showing off the games visuals, which never hurts.
