Professor X (young): because his character arc in the main arc of the movie - lots of unresolved issues from FC that need addressing. Plus, love, love, love James McAvoy.
Magneto (young): total badass, and again, lots of unresolved issues, specifically with Xavier, from FC. And Michael Fassbender is all kinds of awesome.
Mystique: want to see how her character has developed since FC. Plus, she's blue.
Professor X (elder): want to see how his and Erik's plotlines come full circle.
Magneto (elder): same reasons as above.
Sentinels (future): Gotta see what these creepy things do.
Wolverine: Because the last three X-movies I've seen him in, I didn't like (sorry, The Wolverine was meh, IMO). So here's hoping he'll be in a good X-movie.
Blink: Her powers just look so cool. And we need more female X-men.
Beast: Want to see what he's up to, and his interactions with Xavier & Wolverine should be great.
Quicksilver: Haha--just the TV spot made me excited to see him.
Shadowcat: Love Ellen Page--one of the few good things in X3.
Iceman: Awesome powers--his look just rocks!
Sentinels (past): Love how they look so different from the future counterparts.
Storm: I never liked Hallee Berry in this role--good actress, but they need a woman with much more presence for this part. Still, her powers are cool and I really want to see what happens to her from the trailer.
Other characters are background music, there to add to the suspense and cool visuals.
Overall, the Charles/Erik dynamic is what I want to see the most, how these characters develop and what paths they take. Plus, there's a lot of unresolved stuff from FC that has to be addressed. Can't wait!