Mark Snow. The theme. Because whistling is always scary.
The wonderful melancholy underlining the score at the end of Season 1's "Conduit", conveying the despair Mulder feels at being unable to discover what happened to his sister.
The music that was playing during ghostly children scenes in "Closure" by Moby - it was "My Weakness", off his album Play. At the time of filming, Play was on its way to becoming a hit, mainly because Moby gave lots of shows carte blanche in using the tracks for anything (trailers for episodes of Party of Five, incidental music for Buffy, car ads, etc.).
The first X-Files episode to use Moby's work was the Gillian Anderson-directed "All Things," which used "The Sky Is Breaking".
Nick Cave's "Red Right Hand" for the Mulder/Barry chase up the ski lift in "Ascension".
Soul Coughing's "Unmarked Helicopters", which shows up in "Max". It's Source Music emanating from the title character's stereo as Mulder searches his empty trailer: Aside from being a cool-sounding song, it suits Max's jittery, Properly Paranoid state of mind before his disappearance.
Mark Snow's score for "Post-Modern Prometheus" is truly magnificent.
Cher as a favourite singer of the Monster of the Week in "Post-Modern Prometheus" was not a bad choice at all. It feels like going to a fair or disco in The '80s or The '90s. What's not to love?
"Paper Hearts" has great music, somewhat light at times and with dark passages. Indeed very touching.
Say what you will about widely disliked episode "Teso Dos Bichos" (often ranking high among the worst episodes of the series), but its score was insanely magnificent.
'Scully's Theme', the backing music used in season 8 during scenes where Scully is thinking about Mulder's abduction. It's hauntingly beautiful.
The first movie has absolutely epic score. Mark Snow's expanding on the theme and the varying main titles sound divine.
The re-mix of the theme done for the 2008 movie was awesome.
There were two excellent CDs, Songs in the Key of X and the soundtrack of the film. While neither feature much music that was actually heard in the source material note Songs In The Key Of X has five songs that were heard in series, including the full version of Mark Snow's title theme, while the film soundtrack has one song actually heard in the movie itself and two that were only played over the end credits, both albums mainly feature exclusive songs that were specifically produced to fit the overall feel of the show.
The music from the Season 4 episode "Synchrony", partly because it sounds a little more "sci-fi" than most episodes. Appropriate considering the subject matter.
Erik Satie's "Gymnopédie No.1" plays over the opening funeral scene in "Irresistible".
"Wonderful! Wonderful!" by Johnny Mathis really ramps up the creepiness of "Home," though on its own it's an upbeat love song. (It was actually sung in the episode by Kenny James, as Mathis felt the episode was too graphic.)