Let's get on with it!
James Howlett/Logan/Wolverine: Hugh Jackman, of course.
However, should they do a recasting, I'd go with Stephen Moyer, who has definitely portrayed a savage animalistic side in True Blood as vampire Bill Compton.
Wade Wilson/Deadpool: Ryan Reynolds.
Nathan Summers/Cable: Michael Beihn. Who else to bring time travel into the X-Men, than the star of the original Terminator film? And he's already well-versed in playing intelligent badasses.
Neena Thurman/Domino: Katee Sackhoff. She's just so good at playing tough action girls. Just dye her hair black and give her that spot over the eye, and there's Domino right there.
Jack Hammer/Weasel: Jay Baruchel. I saw him picked out on another cast, and I couldn't unsee it. And Baruchel's making his name well in some comedies, which is what the Deadpool movie essentially should be.
Bob, Agent of HYDRA: Daniel Radcliffe. Harry Potter, I say? Well, yeah, this is kind of a left field choice, but he's proven to have some great acting chops (not just in Harry Potter, but also in The December Boys and Equus). And a role as an unextraordinary, unlucky "everyman" character could be a good way to distance himself from the HP franchise once that's over and done with.
Itsu: Kou Shibasaki. She's at a good age for the part, and a great actress too. Just watch her in Battle Royale; she can definitely play strong (even though Shibasaki's BR character was a lot more psychopathic than anything else).
Kenuichio Harada/Silver Samurai: Byung-hun Lee. Lee was one of the few enjoyable things about GI Joe, and he has an amazing physique and the skills (physical and acting) required for a character like this.
Akihiro/Daken: Eiji Wentz. He actually is half-Japanese/half-Caucasian, and at 5'7, actually is a reasonable height for Wolverine's son. My only doubt for Eiji is that I've mostly seen him in comedic stuff (and a few music videos, since he also sings), so I'm really not sure he can play a good psycho. Still, it's nice to dream. Plus, he's cute. ;)
Laura Kinney/X-23: Nina Dobrev. She's recently hitting it big as the lead female in The Vampire Diaries. Unless there's some irrational hatred for anything CW related, she's definitely proven to be a good actress, and can play moody and strong too.
I'm certain I've missed a few characters, but I tried to get as many important ones as I could. Who do you like, dislike? Constructive criticism is welcomed.