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While I can't use them (any background music makes it hard for me to understand my players), I'll recommend several I've found useful for pre-game mood setting:
Tangerine Dream's music is excellent; the best known piece is "Geometry of Shadows" - the main title for Babylon 5. The Bab5 sound track is a good start, but their other albums are equally as useful. And not all of it is instantly "OOH! Babylon 5!"
For religious settings, there are good collections of religious chant; some is online for free. The Presov Choir (http://www.grkat.nfo.sk/eng/music.html) has some Byzantine-Slavonic chant. While vocal, it's excellent, mellow, and mood-setting. Much gregorian is available as well, but the professional recordings are much clearer, and not terribly pricey. ($9 at B&N last I checked.)
Look for "English Country Dancing" music for that renaissance feel. Most of it is actually late medieval, but carried forth into the Renaissance, and was written down then. That the music matches the description given in the older notations of the dances establishes this. The estabished reference is John Playford; many artists have recorded his collection in whole or part.
New England Dancing Masters has several excellent collections of similar folk dance from New England; the steps and terms are the same as English Country Dance, and the music closely related. Chimes of Dunkirk is excellent for Renaissance mood-setting. (I use these at work, but have borrowed disks occasionally to use to mood-set for writing adventures.)
For Spirit of the Century and other games set in the early 20th Century, Glenn Miller sets the big band quite well - it's 1938-on. Herb Alpert and the Tiajuanna Brass is from the 60's and 70's, but harkens back to the Big Band era as well - many players will think it older, and it's pretty good for 60's and 70's stuff.
Carlos Santana has excellent music as well, and a lot of it instrumental.
Find several electronica collections; Russia Electrochestvoi is an old favorite. Lots of Russian classics done on synths.
Anything by Mike Oldfield is good; much of it for an X-files kind of feel. Be warned, tho: Tubular Bells is notorious Trip-toy music, is musically all over the place, and the CD has two tracks... and is a full CD of music.
I'll also mention several to avoid:
Wagner's Ring cycle, Holst's The Planets symphony & Vivaldi's Four Seasons. EVERYONE regonizes them, and lots of people have various movies and TV shows mentally associated with them.
The Music of Star Trek as it's just too heavily associated with Trek. Unless, of course, you're running Trek.
Star Wars sound tracks have the same issue as Trek: most of gamerdom has strong associations with the source, making them useful only for that setting.
Monty Python sound track recordings... tends to trigger silly MP moments. "He's Bleeding Dead Already!"