Some very good recommendations already but I have to mention the following as well.
Miles Davis's Jack Johnson is, in my opinion, his purest album in the rock vein. It's a refinement and development of the music of In A Silent Way and Bitches Brew but is much more stripped down and muscular in its approach. Not a note is wasted and Miles is on some of his greatest form as a soloist (his solo on Right Off is exceptional). Two long tracks full of intensity and vibrancy that just have to be heard. Wonderful guitar playing from John McLaughlin and Sonny Sharrock as well.
Here's Right Off:
http://www.youtube.com/watch?v=DEBKksupBVA (Part 1)
http://www.youtube.com/watch?v=rcFiA-Ny ... re=related (Part 2)
http://www.youtube.com/watch?v=TTJpPnX2 ... re=related (Part 3)
Keith Jarrett's Belonging remains a career high for the man and is also one of the finest albums of the Seventies (some of Jan Garbarek's best work on record as well). Resolutely all-acoustic at a time when fusion was all the rage, this wonderful album has an infectious gospel-fuelled intensity that makes it hard to resist.
http://www.youtube.com/watch?v=EXpPlBFGG_Q (Long As You Know You're Living Yours)
Grant Green was one of jazz's greatest guitarists (before he wasted his talent with fusion in the Seventies) and Idle Moments is his masterpiece. Glorious playing that comes straight from the heart.
http://www.youtube.com/watch?v=mbEwVrDmlxk (Title track)
Sonny Rollins' Saxophone Colossus is one of the great jazz masterpieces. Big-boned and full of life, this is music-making that will leave you with a smile on your face. Immaculate work from the great Max Roach on drums as well.
http://www.youtube.com/watch?v=ox5MUXvh ... re=related (Moritat or, alternatively, the greatest version of Mack the Knife ever)
I have to mention Bill Evans as well. Although Waltz for Debby is probably his greatest work, his duo session with guitarist Jim Hall, Undercurrent, is another masterpiece of understated emotion.
http://www.youtube.com/watch?v=_KRbQrEs ... 1&index=39 (My Funny Valentine)
Another of my favourites is alto saxophonist Art Pepper's album with strings, Winter Moon. Although I am generally no great fan of jazz musicians working with orchestras, this is one of the best examples (along with Stan Getz's immortal Focus) of how it should be done. One of the greatest of musicians, Pepper could break your heart with a few notes.
http://www.youtube.com/watch?v=pJ0jiFC7SX8 (Our Song)
And, finally, I have to recommend something by Charles Mingus as well, whose music was one of my first real introductions to jazz. I was a great fan of Frank Zappa in my teenage years and Mingus was one artist he continually namechecked as one of his biggest inspirations. I still remember picking up Mingus Ah Um and listening to it for the first time. An absolutely extraordinary experience. Although Black Saint And The Sinner Lady is his masterpiece, MIngus Ah Um is probably a better entry point. Bursting with life, it really is one of the most infectious and life-affirming collections of music I know.
http://www.youtube.com/watch?v=WEyETVtEg3A (Goodbye Pork Pie Hat)