I think Destiny's UI has been pretty good in terms of visual style anyway (but it is pretty easy to use as well.) I also like the Uncharted menus for 1, 2. I can't remember how the third one was but I remember thinking that whoever was doing their UI was no longer with them because it didn't feel like it was from the same person. The Last of Us and Uncharted 4 menu weren't bad but it wasn't as stylish as UC1/2.
Someone else already posted this but it reminded me of it; Halo Reach menu was pretty good too.
My favourite would likely be Ridge Racer V's. It looks and animates slick and has a cool soundtrack playing to it. When I first fired it up about a year ago, I just kind of wanted to stay in the menu instead of racing.
Metroid Prime is a given, Final Fantasy XII is a personal favorite, Melee is super iconic and Spec Ops: The Line won me over the moment there was an upside-down flag of the United States and the Star Sprangled Banner in a tenuous note. It's not the most fun game ever but it's super interesting and it's good to remember it.
I've seen many channels dedicated to game music, game openings/intros, game endings, but not game menus, which should get more recognition. So I decided to take matters into my own hands and started making a channel dedicated to showcasing my favorite game menus. I haven't "launched" the channel yet and only have three videos so far, I still don't know I should really go for it or forget it. Feedback is appreciated.