Right on!
Apmonia said:
You will get so many responses to this question it will just become overwhelming. When I asked my friends this same question (all music majors and most sax) the one name that kept coming up was Miles Davis. He is probably the only one artists that (almost) everyone will agree on. Most people will gravitate towards a particular genre or instrument, but Miles Davis' Kind of Blue seems to be a staple in collections. I would suggest to start there.
Apmonia
I can't stress enough how much of an understatement that is. Back in the days of compact discs, I bought Kind of Blue used at the local Hastings, and couldn't keep the tunes out of my head for months.Within a year I had a full 64-disc cd wallet dedicated to jazz cd's. Buy Kind of Blue, and branch out from there.
Personally, I can't stand cool/smooth jazz...but that's another story.
My all-time favorites:
Sonny Rollins-Saxophone Colossus (very powerful sax-easy to get into)
Charles Mingus-Mingus Ah Um (energetic songs with some gospel influence)
Thelonious Monk-Great Hits (normally I don't like greatest hits, but this is one is an exception, quirky and melodic songs that happen to be genius work)
John Coltrane-Giant Steps (very tuneful and accessible)
Jimmy Smith-Back at the Chicken Shack (extremely soulful jazz organ)
Lee Morgan-Cornbread
Charlie Parker-Anything, basically just listen to the guy! (one of the key figures-some say THE key figure-in jazz history, basically invented jazz as you know it today while swing became r and b which became rock 'n roll)
Duke Ellington-Sophisticated Lady (fantastic swing music made by jazz's most prolific genius)
Anyway, that should suffice (those albums comprised about two years worth of listening for me). I very sincerely hope you enjoy them half as much as I do. To recap, start with Kind of Blue and find your way from there.
Happy listening!