"Cave", the starting track in the original game, has a rather happy caveman feel to it that mixes well with the start of a game in the Stone Age with little risk of attack since the game is so early.
"Death", the second track in the original and the first in the Gold Edition, is the opposite of Cave, being quite haunting and almost spooky, befitting of a game that starts in the Stone Age.
"Gamelan", the fourth track in the original and third in Gold, is unique in its use of Indonesian "chime-gongs" that give it a rather nautical feel.
"Rain", track six in the original, feels quite sad and melancholic compared to every other track in the game, giving it a distinct flavour and mood.
"Gray Sky" is notable for featuring the original franchise theme. What makes it fantastic is that the structure almost mimics an actual conflict, with a dramatic first act that implies dispute between two empires, a fast-paced second act suggesting a battle, and a sad third act reflecting the battle's end and loss of life.
From The Rise of Rome expansion:
"Polyester Jammy", second track of The Rise of Rome and the Gold Edition, has a fantastic duet between a guitar base and a flute flourish.
For similar reasons, "Medieval Melody (Mix 2)" in the expansion has a memorable use of the flute as well.
The Credits music introduced in the expansion is wonderfully chill, with a great use of the older instruments mixes with piano and other lounge-style instruments.
From the Definitive Edition:
The release trailer is perfectly nostalgic, starting with the classic "wololo" sound and playing the main theme with a wonderfully-building orchestra. Thank goodness it was included in the Original Soundtrack!
The main menu music which, for the first time for the original game, uses the franchise's main theme, which was originally limited to the intro of the base game and the "Gray Skies" track (the expansion replaced both of these).
"Wonder of the World", the remake of "Cave", is yet another track with amazing strings and flutework. For those who only played the Gold Edition and never got to hear it, starting a new game and hearing this for the first time was a pleasant surprise!
"Caesar's Revenge", the remake of "Gamelan", may play around with the notes and instrumentation a lot, but the second half of the track is, quite simply, beautiful.
Similar to "Caesar's Revenge", "Whirling Dulcimer" (the remake of "Medieval Melody") has a great use of the flute.
More of an awesome inclusion, but Todd Masten saw fit to remake "Sick Sate Rittim", "Polyrhythmic Pong", "String Attack!", "The Old One Sleeps" and "Slow and Spacious Mix 2". What tracks were those, you may ask? The MIDI tracks that were only heard if you played the game without inserting the disc!
Similar to the above, the Definitive Edition now plays through tracks from both the base game and the expansion (previously it was one or the other, or a selection from both with the Gold Edition). Definitely a boon to matches that push past the hour mark.
"Music 10" from Age of Kings, a theme which wouldn't sound out of place for the britons, with its mid-tempo and that wind section line which makes it ideal for sailing.
Several examples on the Conquerors soundtrack, especially the calm "The Bovinian Derivative". It starts with a nice triangle line and some instruments creating the ambience which kicks off around the 1:15 mark, when the main leitmotif of the song is unleashed.
"Defeat" from Age of Empires II: The Forgotten is a sad and mournful melody that really conveys the feeling of watching your empire fall. You can even hear the sounds of hoofbeats at 0:38 which perhaps conveys the victors leading the survivors off into captivity.