I have to admit that the truly entertaining characters were made by other people in games that I ran. A few examples:
(Werewolf: The Apocalypse) A female werewolf in her mid-twenties with a split personality. One personality is a pot-smoking, beginning shaman with major self-esteem issues, and a serious case of delayed adolescence, who started sleeping with an underage, psychopathic packmate. The other personality is a cynical, arrogant assassin with almost no inhibitions, who once gave some of her blood to a vampire in return for some rough sex in an elevator of an Atlantic City casino. The player played each personality to the hilt, including each one hating the other.
(Mage: The Ascension) A Librarian who is also a sadomasochistic mage (Euthanatos) who is a worshipper of the Hindu goddess Kali, and who believes that Kali speaks to her directly. I have actually felt a genuine sense of moral outrage over some of things that her character has done. Her latest hobby is to torture and kill several children, and leave their bodies where they'll be found, until the police determine that a serial killer is in the city, and the media gives the killer a nickname. Once the serial killer has a name, she intends to implant the memories of the crimes into the mind of a completely innocent person so that they'll confess, and will be able to provide details that only the police and the killer would know about. She once put a full length mirror over the bed of an extremely vain vampire that she'd staked (in White Wolf games, staking a vampire paralyzes it rather than killing it), so that the vampire would be able to see precisely how the Librarian was methodically disfiguring her. This incident prompted me to declare to the Player "If I ever end up in the hospital and unable to take care of myself, you're not allowed to visit! I'm afraid of what you'll do if you get bored!"
(Werewolf: The Apocalypse) A werecheetah leading a werewolf pack who is also a fashion model. She once urinated in the luggage of a packmate as punishment for nearly killing another member of the pack. She also conned a werewolf into believing that the way to mark territory in New York City was to leave your teeth marks on the curb, and then curb-stomped him when he attempted to do so. Two quotes from her: "Ugh, I've got NATURE all over me..." (said after walking through a muddy patch of ground while going to a meeting with a high-ranking werewolf). "We're not going to get a speeding ticket, I have tits. Hell, I'm a model, I have PROFESSIONAL tits!"
(Amber) Perdita Angela Vaughn. Not so much an entertaining character as an intense roleplaying experience: The Player played a nine-year-old girl with advanced shapeshifting abilities (including being able to regenerate lost body parts over time) whose backstory was that she had been kidnapped by a sexually sadistic, sociopathic pedophile, who killed her parents and then raped and tortured her for three months. During that time, she'd been forced to choose how her best friend would be tortured to death, and was given a kitten that her kidnapper crushed under his foot once she'd bonded with it. Several times, police showed up at the house she was being held in, only to be mind-controlled by her kidnapper and forced to abuse/rape her themselves. When she was finally rescued (the first game session where this character was played), it took months of roleplaying before she trusted anybody. In the meantime, she believed that everybody was just playing mindgames with her and that, as soon as she felt safe, she'd wind up back with her kidnapper. All of the players and the GM (me) were in tears at the climax of that storyline when she was holding the kidnapper's noble, eight-year-old son in her arms while he died (he'd cast a spell that weakened his father enough to be killed, but the spell also burned him up from the inside, which he knew would happen but hadn't told anybody).
