-Everything involving the Quarian-Geth conflict. This has fascinated me since speaking to Tali in ME1. It ramped up in ME2 with Legion, and the conclusion in ME3 was fantastic. Entering the Geth consensus and hearing Legion expand upon the beginnings of the conflict was great, and hearing him referring to himself as "I" and calling Tali by name before sacrificing himself was one of the most moving moments I've ever seen in any story in any medium. As I've said before, Rannoch is one of my favorite moments in gaming, ever. It really was incredible, and it's made even better with Tali as a romantic interest. Her dropping the L bomb before you call down the strike on the Reaper made a great scene even better, and the unique dialog while sitting down with her on the cliff is wonderful stuff.
-Tali herself. She's been my favorite character in the series behind Wrex, and it's great to see how far she's come. The interactions she has with Shepard if they're in a relationship are really touching. The scene with her drunk is hilarious, too (EMERGENCEEE INDUKSHUN POOOOORT). That final conversation with her in London was some absolutely heart-wrenching stuff. Shame about the photoshopped face picture, though. There were so many opportunities to show her face in-game, but I guess they just didn't want to render it.
-Garrus. He has some of the best scenes and dialog in the game. Shooting bottles with him on the Citadel was one of the moments I've always wanted in the series: a chance to kick back with your close friend and forget about all of the troubles and problems in the galaxy, at least temporarily. I missed the shot... I figured with everything going on (seeing his homeworld burn, his family's whearebouts unknown), he could use a little bit of joy from winning a friendly competition.
-Speaking of Tali and Garrus, being able to thank the both of them for always standing with and believing in Shepard towards the end of the game (before landing in London) was extremely touching and satisfying.
-Tuchanka and Mordin's sacrifice, coming full circle and redeeming himself. "Had to be me. Someone else might've gotten it wrong." As I said, Wrex is my favorite character, and it was great to finally help him out with his race's biggest problem. The bond between he and Shepard was not only that of soldiers, but friends as well.
-Primarch Victus staring out over Palaven, watching it burn.
-Watching Thessia burn after Kai Leng steals the Prothean VI. The feeling of helplessness.
-Liara's VI program that includes your legacy. The conversation in the cabin was one of the most touching scenes in the entire series. Made me feel a little bad that I dumped her after ME1 on my main Shepard.
-Thane's death. His fight scene with Kai Leng was awesome, showing that he still had a little something left in the tank. The prayer for Shepard as Thane passes away was a bittersweet moment.
-Seeing Jack on Grissom Academy and having her slug you across the face instead of a traditional hello. Definitely Jack. Seeing David from Overlord during the same mission was a nice cameo, too.
-All of the squad dialog and chatter. There is a ton of unique dialog depending on who you bring with you on missions. The crew wandering around and interacting with each other on the ship is something I've always wanted, and the game delivered big time.
-Grunt fighting the Reaperized Rachni and emerging from the depths.
-"You did good, son."
-The music. Hearing tracks from the previous two games was great, but the new stuff really is spectacular.