My personal selection of the best and most interesting video game music, something i would recommend classical or any kind of music lovers to give a listen. Many pieces here are quite complex and in my opinion beyond simple entertainment or ambient music, especially the music of Final Fantasy composers Masashi Hamauzu (!) and Nobuo Uematsu, in the Piano Collections, where the game themes were arranged in a classical manner.
Some selections might have been affected by my nostalgia and could potentially not be so interesting musically if you haven't played the game and established a similar emotional connection. Some themes make people cry or swim in a nostalgic flow of memories, most popular themes can be identified by experienced gamers by the first bar or even the first chord and its instrumentation instantly, which in my opinion is another side to the power of video game music.
Note: I don't list the most popular melodies like the Mario and Zelda Title Themes, or the Portal Ending song, because while they are catchy and memorable and part of video game history, they are not that interesting musically. I specifically create a compilation of outstanding video game music that might convince outsiders of its inherent quality.