I love this thread!!
Here's some I can think of:
The horn parts in For No One
The way John's uses his voice in ADITL. Especially the 'news' part. And of course the aaaahhh's.
The way John sounds when he sings 'row' in I Am the Walrus and 'happiness' in HIAWG and the last 'beautiful' in Dear Prudence. Talk about chills.
The guitar intro to Revolution and Paul's scream.
Paul's voice when he sings 'his rival it seems' and 'but Daniel was hot' in Rocky Racoon and the ahhs he adds at the end of corner and revival
The 'Like You' in Love Me Do
The intros to Eight Days a Week, I've Got a Feeling, Sgt. Pepper, and Baby, You're a Rich Man. Man I love the guitar intro to Sgt. Pepper.
The transition of Polythene Pam to She Came in Through the Bathroom Window. That aww look out part and so on is just so cool!
The oh, oh, ooo, yeah at the end of WMGGW.
The ending to I Am the Walrus. The way it builds up is sooo cool. And that chooba chooba thing. What is that?? It's just so cool.
And then I agree with sever already mentioned. The guitar solo in Let It Be as well as Paul's voice in it, Paul's backing vocals in I'm Only Sleeping and Ringo's drumming in ADITL to name a few.
Actually, the entire song Let It Be gives me the chills.