For the most part, I listen to Irish music (both the traditional songs and traditional-sounding stuff, by the Dubliners, the Clancy Brothers and Tommy Makem, so on, and the "modern" stuff, like Clannad and Enya) and Jethro Tull, which I have my mother to thank for, lol...
During the latest FE series, I played the following bits:
-The V'Ger flyover theme from ST:TMP while flying through the Vault
-"You Can't Escape, You Know" - the GLaDOS fight music - from Portal while escaping the Vault
-The "Ridley" theme from Super Metroid (the one used, appropriately, during the escape from Zebes after destroying Mother Brain) during the escape from the Romulan base in Mine Enemy
-"Subject Name Here" - the menu-screen theme music - from Portal while exploring the Reman base in Frozen
I'm still waiting for a method of adding my own stuff to the game's soundtrack without losing the existing cues. If we had that ability, I'd load it up with the expected Trek scores, plus tons of other ambient stuff perfect for space exploration, such as Aphex Twin's Selected Ambient Works albums and a lot of Akira Yamaoka's Silent Hill stuff.
Until then, I'll just listen to podcasts and stuff while I play.
I mostly listen to ambient electronic type music, especially while doing space missions. Stuff like ATB's Trilogy album (the song "Beautiful Worlds" is like an alternate star trek theme to me) and a few Kaskade songs, and a lot of others in that genre. It fits space exploration wonderfully. It leaves something to be desired for the feel of ground missions though...