Recent point & click adventure game "Randal's Monday" has the following character in it:
The game makes references to this character looking familiar and I'm sure I've seen that exact same character in an older point & click adventure game (or maybe something else?) but can't for the life of me remember where.
Best Answer
Day of the Tentacle - it is Harold from the beauty contest (you come across the character when in the future with Laverne):