Anything by The Beatles, The Who, The Doors, The Eagles, Bon Jovi, Barenaked Ladies, Mumford and Sons for some nice background music, though any of them can also be quite upbeat and dancey, depending on the song.
I'm also a fan of The Civil Wars, they're on YouTube and have some amazing vocals.
Jason Mraz, Josh Groban (especially some of his foreign music, it's wonderful), f(x), Laura Wright, Muse, Celtic Women all have a bit of a more relaxing vibe to them.
I'm also a big fan of Beethoven's symphonies (particularly the second movements of Symphonies 7 and 9), Carmina Burana by Carl Orff (O Fortuna being the first and most well-known movement, the whole song cycle is over an hour), any sort of madrigals and chansons by Palestrina, Verdi, de Victoria. L'Homme Armee is always a good song to start with, and any of the various masses based on it.
Mozart had some amazing masses, Bach had some brilliant organ works. Verdi's operas and preludes to them. Debussy, Ravel...I think I'll stop now before I start listing off every historical piece of music I listen to. Which is a lot of them.
Ray Lynch and Enya are also really great for relaxing music. And if you're looking classics, you can't go wrong with any soundtrack by John Williams.