A quick crash course? Hmmmm...
(Not exactly something I do every day, so you may want to brace yourself for spoilers or something.)
Yuuki Rito: The protagonist, of course. Typical nice guy who has trouble with girls, both in behavior and circumstance.
Yuuki Mikan: Protagonist's younger sister. She's mature for her age, and more so than Rito.
Yuuki Saibai: The father. He's a mangaka. Rito often has to go to his studio to help him, or to bring him supplies.
Yuuki Ringo: The mother. She's a fashion designer who's usually overseas, where she's more popular.
Sairenji Haruna: The girl that Rito likes, but can't confess to. And, likewise, she likes Rito but can't confess to him, either.
Sairenji Akiho: Haruna's older sister, whom she lives with.
Maron: Haruna's dog. A proud Boston terrier. ;p
Deviluke Satalin Lala: The antagonist of the story? XD She's the alien princess who falls in love with Rito and who's now worming her way into Rito's heart. Oh, noes!
Deviluke Aster Nana: One of Lala's younger, twin sisters. She can communicate with animals.
Deviluke Bella Momo: Nana's twin sister. She can communicate with plants.
Deviluke Lucione Gid: Father to the three aforementioned girls. He wants someone to take his place as king of the galaxy so he can dump his responsibilities and have fun.
Peke: Lala's multi-purpose constume robot. He can pretty much transform into any attire, but his energy to do so is limited. <_<
Commander Zastin: Royal family bodyguard. He's a bit clueless and has a lousy sense of direction.
Maul & Smutts: Zastin's lackeys.
Momioka Risa: One of Haruna's friends, who has a penchant for groping other girls.
Sawada Mio: One of Haruna's friends. She's much closer to Risa, though, and I don't think the two of them have ever been seen apart. O.o
Jewelria Elsie Ren/Run: They're from a race that switch gender, both in body and mind, with certain stimuli (which seems to happen easier on Earth). Ren loves Lala, while Run loves Rito. Which makes Rito Ren's adversary, and Lala Run's adversary. Yeah. X_X
Tenjouin Saki: The rich, egotistical girl. The kind that goes, "Oh, ho, ho, ho, ho!" At the moment at odds with both Lala and Rito.
Fujisaki Aya: A girl who follows Saki as a loyal servant.
Kujou Rin: Also follows Saki, but rather because her family has served Saki's for generations.
Saruyama Kenichi: Rito's best friend, and seemingly his only male friend. He can be a bit of a pervert, and gets a crush on Yuusaki Riko (Rito's female self).
Golden Darkness/Yami: An emotionless assassin sent to kill Rito, but later procrastinates in killing him for some reason. She can transform any part of her body into a weapon.

Kotegawa Yui: A self-righteous girl who tries to impose the rules and morals of proper behavior on others.
Kotegawa Yuu: Yui's older brother. She doesn't like his behavior much. ;p
Mikado (Ryouko): The school's nurse, who happens to be an alien.
Murasame Oshizu: Once a ghost, is given an artificial body by Mikado and works as her assistant nurse.
Kirisaki Kyoko: The actress who plays Magical Kyoko in the series of the same name, which Lala likes to watch.
Honekawa-sensei: The very old homeroom teacher. (Poor guy. ;/)
Celine: A giant flower from an alien planet, that Lala had gotten Rito on his birthday. Later on... Well, you'll have to read it. ;p
I think I covered everyone worth mentioning. XD I'm sort of writing some fan-fiction for it, so... Those are the basics of what I know. Hopefully not too revealing. <_<