He is the only character that cannot max out all of his skills, as each of his skills have five levels and the max character level is 18 (18 points for a total of 20 possible ranks).
He is the only character without an ultimate. Karma has an ultimate, albeit one that doesn't follow the normal rules applied to ultimates. Udyr, however, has 4 skills that can be leveled up to the maximum rank of 5.
Udyr is one of a few champions to have multiple textures in one skin. Udyr however has the most different textures in one skin than any other champion, as he has a different one for each of his stances.
Udyr's dance shows the Drunken Master Kung Fu Style.
The word "Udyr" literally translates into "Beast" in Norwegian. The Danish words "Uhyr" and "Dyr" mean "Monster" and "Animal", while "udyr" is mostly used to describe people as evil, acting like animals and not caring if they kill.
Udyr is one of two champions that went into the weekly champion rotation on the day of their release. The other one is Poppy.
Udyr was one of the champions chosen for the Ionian pool available during the Ionia vs. Noxus match. He was one of the selected champions, and was voted the MVP.