As of November 2013 there were 17 characters that were introduced at one point into the game, but were limited-time. Meaning, if you didn’t purchase/earn them during the event you won’t be able to get them ever (unless EA re-releases them).
Limited-Time Characters:
All characters listed below are no longer available. Click on the character for more details.
Halloween 2012
Raven
Burns Monster
Kang
Mayan God
Talking Krusty Doll
Christmas 2012
Santa Homer
Valentine’s Day 2013
Shauna
St. Patrick’s Day 2013
Tom O’Flanagan
Leprechaun
Wacking Day 2013
Lumpy
Pet Snake
4th of July 2013
Rex Banner
Abe Lincoln
Halloween 2013
Suzanne the Witch
Booberella
Frog Prince
Items from Halloween 2012 (except for the Mayan God) returned in 2013
Thanksgiving 2013
Tribal Indian Chief
Christmas 2013
The Yes Guy
Mr. Costington
Christmas Raccoon
The Grumple
Candy Kevin
Snow Monster
Plow King (Skin for Barney)
Mr. Plow (Skin for Homer, Returning from 2012)
Santa Flanders (Skin for Ned)
Ebenezer Burns (Skin for Mr. Burns)
Married to the Blob Episode Tie-In
Kumiko