Kicking off my Episode VII character wishlist is hero of the Alliance (or Rebellion, depending on which side you're on), Wedge Antilles. Why? Because he has two Death Stars etched onto the side of his X-wing starfighter. And if that isn't reason enough, his exploits in the Star Wars expanded universe are legendary, with an impressive track record from leading the New Republic's Rogue Squadron to name but one of his accomplishments. Despite being one of few characters to be present at both the Battle of Yavin and Battle of Endor, he's had surprisingly little screen time and surely deserves more.
Mon Mothma became Chief of State of the New Republic in the expanded universe, but we didn't get to see much of her in the movies. Aside from briefing the Alliance forces during Return of the Jedi, she was originally supposed to be introduced as one of the founding members of the Alliance in Revenge of the Sith before her scenes were cut.
While we are unlikely to see anybody from the expanded universe make an appearance, there are a plethora of original characters that have never been seen on screen. Episode VII writers could do a lot worse than choose to include one of the following.
If an Imperial remnant plot emerges, I would love to see the likes of master tactician Grand Admiral Thrawn who rallied the disarrayed Imperial fleet in the wake of the Emperor's demise. He had a very different leadership style to Palpatine and Vader, encouraging creative solutions rather than executing harsh punishments for failure.
As for a new Jedi Order style story, you don't get much cooler than Kyle Katarn, titular character of the Jedi Knight series of classic LucasArts video games, who started as a rebel operative and learnt the ways of the Force after discovering his Jedi heritage. Katarn is not your average hero, and initially fell to the dark side until he accepted was invited to join Luke Skywalker's new Jedi Praxeum, and even then was often criticised for veering off the path of the light side of the Force.
I can't really mention characters without talking about one I, and probably most other sane people, am not interested in seeing again: Jar Jar Binks. I don't think I need to explain.