If you've never seen a Newman film then I suggest that you rectify that forthwith. I know that a lot of people turn their noses up at old films these days (heathens!) but there are some true gems out there. Chances are that you won't be able to find them in your local Blockbuster but if you're signed up with an online rental company then they should be easy to get hold of and if not, just take a gamble and buy one from Ebay or Amazon. I heartily recommend The Sting as your starting point. It's a joyous film; one of my all-time favourites. Newman and Redford have brilliant buddy chemistry, the plot is clever and the feel-good factor enormous. If you like that then Butch Cassidy and The Sundance Kid should be your next stop. You may have guessed that I have a bit of a thing for the Redford-Newman combo.
Personally my next port of call is Cool Hand Luke. It's one of Newman's most iconic roles and it has taken me far too long to get round to seeing it.
Frank Sinatra may be the official 'Ole Blue Eyes' but I'll take Paul Newman anyday.