My predictions (which were made last Friday, before Game 1 of each series):
Ducks in 5. Giguere is unstoppable and the Wild have outlasted their luck. They're tired, they're worn out, and they're outclassed.
Devils in 6. Tough call here, but the Devils have patience and won't take too many stupid penalties. Senators just don't look like they want to win.
The Cup: Devils in 5. The Ducks will take the first or second game away from the Devils as New Jersey underestimates them. The others go to the Devils, and they celebrate in New Jersey after game 5.