My vote goes to Linda the Hulking Lungfish of Lake Oblongata in Psychonauts. Easily the most emotionally affecting performance from a lungfish to date.
Otherwise, it's gotta be Sander Cohen from BioShock. "I want to take the ears off, but I can't. I hop, and when I hop, I never get off the ground. It's my curse, my eternal curse! I want to take the ears off but I can't! It's my curse! It's my fucking curse! I want to take the ears off! Please! Take them off! Please!"
Pretty much any BioShock character sets a new standard for game acting, but Sander Cohen's performance was my favorite by far.