Sammy Davis Jr. for sure...and if you like these guys, you MUST check out Rat Pack stuff! I laugh so hard when I listen to them!
Andrew Sisters
Bing Crosby
Andy Williams
Ella Fitzgerald
Louis Armstrong
Mills Brothers
Ames Brothers
Nat King Cole
Perry Como
Tony Martin
I'm hesitant to put Tony Bennett. He was in the same era as Dean and Frank and a lot of people love him, but he's not my style. I'll leave it up to you to decide.
As for newer artists with the same style - Michael Buble (Pre "To Be Loved" album) and the Puppini Sisters
Actually, being a fan of Dean Martin, I started to like big band as well - Guy Lombardo, Glenn Miller, Benny Goodman, Count Basie (Frank Sinatra actually sang with the Count Basie band before he really hit it big)
As for good songs - I like Frank's early work "Come Fly With Me" "Chicago" "Bewitched" etc. As for Dean Martin, choosing good songs...how many you want? Almost any song by Dean is good. I'm a huge Dean fan. My favorite is a later song by him "Honey," but the "Essential Dean Martin" CD is probably a good one to start your collection.
Also, if your a Dean Martin fan, you might want to check out the Martin and Lewis radio shows, Colgate Comedy Hours, Dean Variety Shows and Dean Martin Roasts. Those are pretty funny. In the Martin and Lewis stuff - Dean is genius as a straight man.