I've never really listened to much Jazz so please recommend some CDs. Thanks.

You need to give some idea of the kind of music you like. Surely you've heard some Louis Armstrong, Frank Sinatra, Ella Fitzgerald, some big bands? Presumably you like piano and want to hear that? Other instruments or groupings you like? Do you like rock n roll and maybe fushion? It's best to start listening to stuff you are more likely to like at the outset.

When I starting listening to jazz, I was a fan of classical and rock. So I found that Keith Jarret's solo concernts (Koln was the big one at the time) reminded me of the sound of classical piano, but was jazz. On the rock side, I started with Return to Forever, Chick Corea's "fusion" jazz band.

Rather than spend money on CDs you're not sure you'll like, why not try the old-fashioned approach - radio? If you don't have a good local jazz station, there are plenty online (WBGO out of Newark, for one), plus Sirius. You'll get some variety and find out for yourself what you like.

If you get the App "Jazz Radio" for your computer or smartphone, you can get your ears wet with the different dialects of Jazz. When I was young, there was a collection called "The Smithsonian institute of Jazz" that had everything from WC Handy to Miles Davis. Don't know if this is still available. When I first started listening to jazz, I listened to Freddie Hubbard's "Red Clay" back and front until the LP was grey in color. You will find what most appeals to you and follow it. I hope this helps you. Happy listening!

Doubletime Records has a great list of the 100 Historically Significant Jazz Recordings If it is the same list they had 20 years ago (and it looks like it is) this list became the foundation of my collection. They even have a button to add all to your shopping cart!

I agree with the recommendation above to listen to the radio, probably streaming these days. My local jazz station KCSM is pretty good and they stream on the Internet. Everyone has slightly different tastes so this is the best way to find yours. I personally like the Blue Note catalog from the 50s and early 60s.

If you have Spotify installed I could pass you links to some of my lists. I remember when I began to buy/burn my first jazz albums and compilations, 25 years ago. Some of that music was irritating, then, but now that my "ears" understand a little more, it's very pleasant. The first recordings I bought were totally different worlds: "A lift to the scaffold" from Miles Davis, and "Affinity", from Bill Evans and Toots Thielemans. I still love both of them.
There was a compilation of Duke Ellington sessions for the BBC that is great, too.
If I had to select just three, randomly:
-"Time will tell" (Wynton Marsalis/Jazz Messengers. Brilliant hard bop, happyness made music.
-"Places" (Brad Mehldau).
-One whose name I can't recall now (edited: "You are there"), it's from Hank Jones and Roberta Gambarini, it's a gem.

That Double Time list is terrific for what it is, but with its admitted emphasis on the bebop era, it neglects a lot of the great jazz that came earlier (and later, for that matter, though my tastes run more towards the older stuff).