KateModern: Terrence is a brilliant character. He's basically a sociopath, but he gets enough Villain Episodes and Strange Bedfellows scenes that that doesn't matter, and he somehow manages to be both hilarious and terrifying, often simultaneously.
Though Penny, surprisingly, is the one who gets the most backstory. Combine that with Felicia Day's adorableness and, well, there's not much more to say, is there?
Jack Bulletproof, the Cop Who Plays by All the Rules. Because police procedures are there for a reason, and anyone who manages to be this awesome while doing the most reasonable and thought-out thing in any given situation deserves a mention.
The Nostalgia Critic: So messed up... and so entertaining to watch. Also, his singing voice. Dear God, his singing voice.
OH MY GOSH, CHESTER A. BUM IS THE GREATEST CHARACTER I'VE EVER SEEN IN MY LIFE! He's deranged, stoned out of his mind, and absolutely hilarious.
Atop the Fourth Wall: LINKARA! He is a man! -PUNCH- Wears a purdy hat!]] Quoting theme songs aside, not only is he a master of snark, but I also end up cracking up from his rage outbursts.
I don't know whether she counts as a "character" or not, but SCP-811 is one of the best written SCP items on the site by their own standards and EXACTLY how you should write a dangerous humanoid SCP item. She's got strangeabilities that, while cool, don't come off as "super powers", she's dangerous without being malevolent, in fact she can be quite sweet, and she even has a backstory that makes you feel bad for her. It's a shame she doesn't get as much attention as SCP-173, SCP-682 or even SCP-105.
I like SCP-085 a lot. She's so nice!
Eugene, Matt Santoro's clone. He can make it snow with his warlock powers, he's a badass with his lightsaber, and is easily the funniest character. Need proof that he's the funniest character? In How to be Popular, Matt teaches him how to be popular (hence the title), and tells him to express his style. So, he dances to the song "Sexy and I Know It" by LMFAO, and he even twerks! That's comedy gold.
Korak from High Rollers. After being a figure shrouded in mystery thanks to some great storytelling and the two utterly opposing views of him (a slave owner and oppressor vs a champion and a hero), the former view turned out to be a misunderstanding and he turned out to just be... a genuinely Nice Guy, hailed as a hero, yet who is too ashamed of his past to tell of it, and of his real name to even use it - which is heartbreaking. The fact that instead of using his 'hero' status to be an ass and brush off Jiutou and her allegations, or even have her locked up for attacking him in an important fight, he let her go on her way and later sat down to have a rational conversation and address the issues raised with an uncommon and touching frankness and honesty does him credit. In addition, he has a humility about him (seen in his interaction with Jiutou in episode sixteen 'I did not want to disturb you with my presence...') which is utterly adorable, and a sense of humour (or at least a will to save face for Cam) as seen at the end of the same episode. And to top it all off, he is a seven foot tall red-and-gold humanoid dragon paladin, clad in golden armour and wielding a mystical crystalline blade.