We have a thread on character quotes, so here's on on character nicknames and/or Here are some to start off:

Donna Jo Tanner: DJ (of course!), Deej, Tennis Ball Head (by Danny when she was a baby)
Stephanie Tanner: Steph, "Step On Me," Dawn (last two in the eppy where Joey goes to Hollywood to film the pilot w/ Frankie Avalon and Annette Funicello)
Michelle Tanner: Princess Michelle (in the night before first day of kindergarten dream sequence), Shorty, Munchkin (by Jesse)
Daniel Tanner: Danny (of course!) Dirty Dan (the eppy where he played poker), Manny Tanner (his made-up evil twin who cancelled a date with the Honeybee Mom in season 1), Mr. T (by Kimmy)
Joseph Gladstone: Joey (of course!) Joe (in the season 1 eppy when he gave up comedy to become a businessman), Cartoon Breath (by Jesse), Walrus (when he was a kid), Joe Stone (on "The Perfect Couple")
Hermes Jesse Katsapolis: Jesse, Uncle Jesse (of course!) Uncle J, Doctor Dare (by his friends when he was 20), Vulture (when trying to change his music biz image) Jesse Cochran (season 1)
Rebecca Donaldson Katsapolis: Becky (of course!) Beck, Aunt Becky, Low Board Donaldson (when she was a kid and afraid to go off the high dive)
Kimberly Louise Gibbler: Kimmy (of course!) Gibbler, Kimmy Gobbler, Kammy (by DJ's cousin Steve and by some junior high girls at her surprise birthday party), Kimmy Gibbleburger (by Stephanie)
Nicholas Katsapolis: Nicky (of course!), The Twins (collectively, with Alex)
Alexander Katsapolis: Alex (of course!), Big Al (the episode where Jesse mixes up the twins), The Twins (collectively, with Nicky)

Did you notice Kimmy never called the little sisters by their real names? She called them "squirt" and "kid". When Steph was older, she called her Blondie.

Dont forget Joey was called Ranger Joe in season 5.

Michelle was called Trail Mix by her friends on the camping episode.

Danny was also Mildew in one episode - He tried out for Jesse's band

kimmy was also called cammy or kammy in the episode where dj had a party for her, and kimmy brought her two older friends called melissa and nina. they wanted to trash the tanner house.

also, vicky called kimmy "kimmy gilbert" in one episode

Kimmy called Jesse "Hairboy"