The Good Ending Theme. A heartwarming soundtrack for a heartwarming ending. Sadly, this ending isn't the canon one for this game, as Last Light shows.
The Tower sums up Metro's bleak, oppressive setting perfectly. It's also playing during the game's prologue. And in Redux, it even plays during the final approach to the titular Tower.
Market. Probably the most awesome music from the first game's entire soundtrack. So much, that it plays repeatedly throughout the game on various levels.
Riga. A comfy jazzy little tune that plays in Riga's bar where Artyom and his travel companions drink to celebrate their survival. It's a perfect contrast to the bleak existence that is life in the Metro.
Chase. An awesome piece that plays during the climax of the game's story, where Khan and Artyom fight Red Line soldiers on railcars and a moving train, all while trying to secure the Baby Dark One and preventing him from falling into General Korbut's hands.
Bunker Blues, like Market before it, is a rather catchy rock tune that plays several times throughout the game.
Redemption, the good ending theme. Like the good ending theme of 2033, it's a soundtrack that perfectly captures the heartwarming and tearjerking parting between Artyom and the Baby Dark One. And unlike the former, this one is the canonical ending of the game.
Into Sunset, the bad ending theme. An absolutely tearjerking ending theme that plays when the Baby Dark One says farewell to Anna, as Artyom blows up D6 in this ending.
Enter The Metro, the main menu music captures the atmosphere of the plot (and setting) perfectly with a quiet and mysterious start, continues with a melancholy guitar part that transforms slowly into a electric guitar crescendo only to fall back to the melancholy guitar.