Update June 2011: Peter Dinklage is doing an excellent job as Tyrion. Most of my favourite scenes in the tv show so far have been the ones with Tyrion and Bronn in it. The only other movie I know him from was Elf, where he was the "angry elf". He's also been in Narnia but I can't remember his character there since it's been awhile since I've seen it. Nevertheless, I wouldn't be surprised if he wins awards for is acting performance as Tyrion.
Back when I was reading the books, I imagine Tyrion as the actor who played Willow, Warwick Davis.
Tyrion Lannister in A Song of Ice and Fire is a misshapen dwarf nicknamed "The Imp" and "The Halfman" who was despised by his father, Tywin and sister, Cersai. Though Tyrion shared his father's talent for political maneuvering, he received little respect from Tywin because of his deformity, sharp tongue, penchant for whoring, and the death of his mother during his birth. He is capable of cruelty to his enemies, but also has great sympathy for fellow outcasts and the mistreated.
Early in life, Tyrion found himself ostracized from regular family life, and sought his own entertainment. When Tyrion was 13, he and his brother Jaime rescued a common girl, Tysha, from a compromising situation. Tysha found Tyrion pleasing, and they wed in secret, but when Lord Tywin found out, he explained that she was a prostitute whom Jaime had hired for Tyrion's benefit. His father then had her gang-raped by a barracks of his guardsmen before Tyrion's eyes, and then forced the boy to do the same; while each of the guards paid Tysha a silver coin, Tywin gave Tyrion a gold piece instead, because "I was a Lannister, and worth more." This incident scarred Tyrion mentally, but also brought him closer to Jaime, the only person who ever showed kindness to him.
I imagined that guy from Willow to be Tyrion, as I wasn't really familiar with short people apart from him & Mini Me from Austin Powers. I soon found out the actors name was Warwick Davis and didn't realize that he's appeared in a lot of popular movies including Harry Potter.