Suspect: Petyr Baelish, a.k.a. Littlefinger
Why He Could Be the Killer: Littlefinger is the ultimate creep, lusting for all the power. Killing a king would satisfy that lust.
Suspect: Olenna Tyrell, a.k.a The Queen of Thorns
Why She Could Be the Killer: Sweet little Olenna is not someone we'd want to mess with. The Tyrells are all about girl power and it's unlikely Olenna thinks Joffrey is a suitable match for her granddaughter, Margaery
Suspect: Tywin Lannister, Hand of the King
Why He Could Be the Killer: If Tywin kicks his grandson off the Iron Throne, the next in line is Tommin. Young Tommin would be much easier to manage than the power-obsessed Joffrey.
Suspect: Tyrion Lannister, a.k.a The Imp
Why He Could Be the Killer: Oh we hope it's Tyrion. After putting up with the incessant insults from Joffrey, Tyrion would be well within his rights (we say) to kill the King.
Suspect: Sansa Stark
Why She Could Be the Killer: Why shouldn't Sansa kill Joffrey? He had her dog killed, her father beheaded (then made her look at it), and then tried to have her raped (we think) before Tyrion put a stop to it. We hope Sansa killed him. Also, what's with the necklace?
Odds: Unfortunately, only 4/10
Suspect: Ser Dontos Hollard
Why He Could Be the Killer: Again, this guy deserves to kill Joffrey. The King made Dontos look like a fool during Joffrey's name day celebration. Also, what's with that necklace he gave Sansa?
Suspect: Lord Varys
Why He Could Be the Killer: Varys has ears, eyes, and people everywhere around the realm. So how hard would it be for Varys to poison someone? He always wants what's best for the Realm, and clearly Joffrey is not that.
Why She Could Be the Killer: If you can't see why, then you're some kind of wrong person.
Suspect: Margaery Tyrell
Why She Could Be the Killer: Margaery is a "good" person -- but she's also very cunning. We can't imagine her really wanting to be married to Joffrey, so we'd support her if she decided to murder the douche.