Jimmy Two-Teeth is a rat who lives in a wall in the office in Sam & Max Season One.
After his attempt to kidnap Sam & Max's phone in Culture Shock ends up with him being dropped out the window, he mostly avoids them to go about his own business. Still, their paths repeatedly cross in ways that end badly for him.
When the Maimtron 9000 breaks down at the start of Season Two, he uses the opportunity to rebuild it as a casino and take up residence there. In Ice Station Santa, Jimmy turns out to have an wife and son, and Sam & Max have to save their Christmas (or rather, prevent themselves from ruining it).
He was/is an excellent boxer (mainly because the ability of wielding a human-sized boxing glove). His full name is "James Tiberius Two-Teeth".
Jimmy is never seen in The Devil's Playhouse, but mentioned in The Penal Zone. Max hinted that Jimmy and other rats carried a plague, securing Max's re-election, and was bought off by Max to go into hiding.