Can you recommend Jazz for some one that doesn't like Jazz?

I took it upon myself to learn to like jazz about ten years ago, and it has now become my primary genre. Lots of great recommendations here. In between sampling those, I would recommend finding some higher quality jazz stations and let them play. As you hear things you like, explore those artists further on your subscription platform of choice. 

Here are a dozen titles I consider a "Jazz Starter Kit:"

1) Dave Brubeck - "Time Out"

2) Miles Davis - "Kind Of Blue"

3 Duke Ellington - "Live At Newport"

4) Duke Ellington - "Blues In Orbit"

5) Lester Young and Teddy Wilson - "Prez And Teddy"

6) Oscar Peterson - "We Get Requests"

7) Monty Alexander, Ray Brown, and Herb Ellis - "Trio"

8) Bill Evans - "Live At The Village Vanguard"

9) Ella Fitzgerald and Louis Armstrong - "Ella And Louis"

10) Stanley Turrentine - "That's Where It's At"

11) Vince Guaraldi - "Greatest Hits"

12) Ahmad Jamal - "At The Pershing/But Not For Me"

The suggestion to get a guidebook on jazz recordings is the way to go.  A book like the All Music Guide to Jazz not only lists most of the major artists and their recordings, it has a decent rating of each recording so you can sample the best. 

The recommendation of the Ken Burns documentary series is also very good because it places the music in a social and historical context and employs narrators who know and love the subject and convey what the music means to them.  The series is long but it is rewarding.  The biggest problem for me was that the series stopped well short of covering what would have been at that time current jazz artists and their music; it was mostly ancient history then, and more so ancient history now.

If you want to hear a decent cross section of jazz development at a particular time, and appreciate how advanced jazz performance was quite a whiles back, sample the top recordings from just one year--1959.  Three giant recording came out that year:  Miles Davis "Kind of Blue," Dave Brubeck "Time Out" and Ornette Coleman "Shape of Jazz to Come."  Of these three, my favorite is "Shape of Jazz to Come."  

If you have an internet radio tuner there are hundreds of jazz stations to sample various types of music.  A lot of us like different forms [not hard to tell that].  Lee Ritenour is an excellent guitarist a is Peter Frampton  [yes indeed] "Fingerprints" or "Frampton forgets. the words".  

I'm surprised that no one has complimented stuartk for his thoughtful and detailed response!  The first albums that really drew me into jazz were Kind Of Blue (Miles Davis, already mentioned) and Giant Steps (John Coltrane).  Louis Armstrong (Satch Plays Fats) is another easy recommendation!