I truly think that Harry Connick Jr. is the Frank Sinatra of my generation (or maybe tecnically a generation ahead 8^D). He has such a smooth voice, but lots of style, and can puts his own New Orleans flair on a lot of songs he does. Here's the very first song I heard by him, and it made me fall immediately in love with him.
It was a late night after a youth group outing and we were all waiting for our parents to pick us up. I was just getting into jazz music, and had heard instrumental stuff, but nothing vocal yet. So late at night, watching the stars in the hatchback trunk of my friend's car, he put on this album. First I'm greeted with some nice mellow swing, followed by a screaming trumpet [AMAZING], then a smooth voice, and the rest was history.
Harry has put out a LOT of albums since then, and I own quite a few of them, and it is great to see how his style has progressed, but stil kept that "classic" feel.