Red Dead Redemption - I really felt I was in the old west. There were newspaper updates throughout the game, over 40 animals, very realistic settings, Ennio Morricone inspired score, well grounded characters, dynamic weather effects, NPCs doing different tasks, working trains, and a real sense of scale.
Vice City - Felt I was in the 80s literally. Every radio station song and commercial were perfect depictions of the 80s. The sunny beaches and neon colors made me feel I Watson vacation. The world design was very intricate and had me memorize item locations and landmarks very easily. I never was lost later in the game, whereas I still get lost in other GTAs.
Donkey Kong Country trilogy on SNES - Mainly for the music in the first place. Each game I felt I was on some exotic adventure. The world maps really pull me in as well and feel cohesive. Levels have layered backgrounds and set up locations very unique. The whole kremlin gang led by K. Rool had a menacing and hold on the trilogy. Love the Kong family and how hey felt like a real family.
Banjo-Kazooie - The game is like one big fractured fairy tale. The themed worlds are brought alive by the zany cast of characters and enemies. Gruntilda has an always nagging presence. Kirkhope compose a cohesive score which dynamically shifted based on what area of level you were in. The levels aren't too huge where you get lost, but just right. The British humor really sticks out.
Ocarina of Time/Majora's Mask - what hasn't been said
Super Mario Sunshine - Mario on a beach resort island cleaning up goop. The interactive levels and themes made the game really cohesive. A Mario game grounded partly in reality with retaining its fantasy like wonder