My list of favorites spans way more than this, I believe, but hey, you just asked for ten, and so the list below; with the list comes a series of fairly insufficient, but hopefully still useful, recommendations. I chose them by a meek and disorganized introspective, with my criteria for choosing being based on how much they make me have, er, stirrings when I listen intently to what I consider are their most emotive songs. Note that this doesn't include my favorites in the Classical world, since that doesn't seem to be the main point in this thread; though I might make a list for that later on, in this same thread.
1.) Björk - Listen to her album Homogenic, and there's a massive chance you'll get where I'm coming from. Everytime I listen to that album, I feel like I'm gazing into the heart of my personal abyss....Her voice is a bit of an acquired taste, though, or at least that's how I took it. The most accessible aspect of her body of work, however, would have to be her first two albums, Debut and Post, so if you're not sure about her whole artistry that much, go for those two albums first.
2.) Joni Mitchell - And to her, the album Blue. Her writing is wonderful, and is definitely the hallmark of her music; if you're gonna listen to that album, or, in fact, to any of her albums or singles (excluding, perhaps, Mingus, and the more experimental Jazz-fusion albums after that), the best experience is to be got by honing in on the words. Court and Spark and Clouds are also exceedingly fair representations of her work.
3.) The Beatles - Of their relatively massive oeuvre (fourteen not-just-compilations albums in ten years!), my favorites would have to be the albums Rubber Soul, Sgt. Pepper's Lonely Hearts Club Band, Revolver, Magical Mystery Tour, The Beatles, Abbey Road, and the singles Hey Jude/Revolution, Paperback Writer/Rain, Get Back/Don't Let Me Down, and Across the Universe. Production wise, The Beatles were delightfully novel, though the words of their songs are definitely just as important, especially for the songs Something, Hey Jude, and, *teeheehee*, I Am the Walrus. (Little note: Listening to the Beatles' Sgt. Peppers feels rather incomplete if one neglects the Beach Boys, a relatively big influence to said album. When you're gonna listen to Sgt. Pepper's, try listening to the Beach Boys album Pet Sounds beforehand)
4.) Ella Fitzgerald - Her voice is absolute perfection, period. Nope, period. End of discussion, get out of my face [xP]. Check out Ella Fitzgerald Sings the Cole Porter/George and Ira Gershwin/Duke Ellington Songbook if you wanna catch a strong taste of her, though I myself got hooked with her collaboration with Louis Armstrong, Porgy & Bess.
5.) U2 - Their songs and albums just....run through me like....like a river....or something. The mixture of "sweeping" and "ambient" in their sound, coupled with their generally abstract or topical lyrics, makes their music exceedingly powerful. My favorites of theirs would be the albums The Joshua Tree and Achtung Baby. (Little note: Liking these guys generally means liking (however shallowly) Coldplay, since the parallels are generally unavoidable: I suggest succeeding a "session" with The Joshua Tree by listening to Coldplay's Viva La Vida, or Death and All His Friends)
6.) Nina Simone - Her mixture of Jazz, Blues, and Classical music is spellbinding - appropriately, if you wanna get a good feel of her work (as closely as I did, at least), listen to her album I Put a Spell on You, though a better gauge into her talents would be her very first album, Little Girl Blue.
7.) Daft Punk - I consider the music of these two guys my official introduction into modern pop music, and so, regardless of the actual value of their work, I take their music very closely to my heart. But then, the actual value of their work, as with all artists (to the appropriate audience), exceeds goodness, especially with their latest album, Random Access Memories (from which the single Get Lucky came from).
8.) Enya - Her music is that special "place" I retreat to whenever I need to relax, to take a break from all that emotion and just re-energize my mind. The general ambience of her music is best captured by her second album, Watermark, which contains her most familiar song, Orinoco Flow. (Little note: Also, she's the one who sang the song May It Be for the first film in the Peter Jackson film treatment of The Lord of the Rings)
9.) Janelle Monáe - Listening to her songs means a whole night of dancing for me; her music is absolutely infectious! And yet, if you dissect much her music, you end up getting an epic narrative (her official works all tackle the sage of an android named Cindi Mayweather), a highly thoughtful examination of the nature of cultural prejudices (the saga tackles a lot of fairly complex themes, such as the idea of love as related to gender [and such], and Afro-centrism), and a well-made survey of the world of Rhythm & Blues (her albums are outstandingly eclectic). Best to follow her music chronologically, starting with the EP Metropolis: Suite I (The Chase), then with the albums The ArchAndroid and The Electric Lady.
10.) Kimbra - She takes pretty much the best parts of most of the artists I listed here, and mashes them up into a wonderful, and oddly original, plethora of pop sounds. She's only released two albums so far (Vows and The Golden Echo); catch both of them if you can. Though, if you don't know her, you've probably already heard her voice: "Now you're just somebody that I used to know...." (She was the girl).
