I've been doing a lot of research lately on what are called Alternate Reality Characters (ARCs). As I can best describe it, an alternate reality character is a fictional character who "interacts" with real people on social media platforms. I discovered the term when I was browsing online for information about - what else? - Glee, and read it on the discussion board for Quinn's Facebook page.
This page, specifically created by Fox to promote the show (It's linked to Glee's official Facebook page, as are the other characters' pages) depicts what the characters would say and think based on the storylines of the show. Other television favorites of mine, such as The Office and 30 Rock, have similar accounts both on Facebook and Twitter.
I could spend hours reading the blogs and tweets of my favorite fictional characters. In addition to those created by a show's writing and/or marketing departments, fans worldwide create thousands of "unofficial" accounts (called RP accounts). I enjoy reading how they interpret fictional characters as well. In my opinion, the best accounts make you feel like an insider in the fictional world. Some of my favorites include:
AMC's Mad Men - on Twitter Mad Men's fourth season just started, and this site compiles the best tweets about the show, including fictional character accounts, the official MadMen_AMC account, and fan commentary.
This link is good also: http://guestofaguest.com/television/ask-a-mad-man-theyll-answer-on-twitter/
Gleeks should look at this database of Glee Fictional Character Accounts: http://www.gleetwitter.webs.com/. If you'd prefer to follow the actors themselves, @GLEEonFox has a list of them as well as official fictional character accounts written by the Glee writers: