One of the greatest personalities I ever played was an ogre named Boneless. The name comes from the fact that in his language he was called "spineless" by his mother and cast out of his family. Though losing meaning understanding in translation it came out in common as Boneless.
He had an intelligence of 7, for which I intentionally lowered despite what I rolled. A fighter by class, chaotic neutral by alignment.
A common theme of this character was his obvious lack of intellect. In fact when meeting people he would ask "Are you friend?". If they answered "no" he would kill them outright, because "not-friends" as he put it were bad. If you said "yes" then you were friend for life, and then he would say "If anyone hurt you I eat their face." So his life was a very black and white outlook on things.
He liked to sing, although if you can imagine an ogre singing. He had a greatsword and a pair of boots of striding and springs that the wolf man gave him. The story of the wolf man which told his companions came from when he was walking through the woods and saw a man in armor fighting a "puppy" (a dire wolf). Seeing as the man was being mean to the "puppy" he decided to smack the man and tell him he was being bad. Unfortunately he his so hard the man, wounded from battle, fell dead. Boneless slowly approached the "puppy" to see if he was okay, because he wanted to pet him. That was when the "puppy" turned into a man, a druid to be exact. In thanks for Boneless saving this man's life he gave him the sword that was on the fallen foe, and his boots. The "Wolf Man" told Boneless the boots would ease his travel, and the sword he could use to defend himself should anyone attack him. Happily accepting of these gifts, Boneless and the "Wolf Man" parted ways.
He even talked about his worship of "The Moon Lady". "The Moon Lady" was actually a priestess of Luna who came across Boneless while she was out on a vigil. Boneless was out late and was hungry, and smelled food so he began to head that way. Unfortunately this headed him to a village, where he was driven off by the local militia. The priestess came across the big lug, laying out in a open field, not far from the village. Curious she approached noticing his wounds, a she felt no evil from the creature and decided to heal his wounds. Upon opening his eyes he looked straight up seeing the priestess. The moon was fully, and was directly behind her head and seemed to form a halo about her. No one in his life had ever been so nice to him before, so Boneless in his logic figured this must be some kind of god. From that moment forward he worshipped the woman he called "The Moon Lady". Though he never saw her again, every full moon he would go out in an open field and sing to her, in thanks for saving him that very night.
This character was a combination of comic relief, a voice of wisdom to his party, and even a point of common sense. Comic relief was obvious, but the wisdom to his party was found in his simple view on things. The common sense came from his actions. He spoke with action not necessarily with word, and playing him almost child like was fun. Low intelligence characters are easy and fun, they believe they can do anything because they don't know otherwise.