A list of games featuring polyominoes, presented in roughly chronological order. I've also included other polyforms like polycubes and polyhexes. Please add any that I'm missing. also, if you know which ones of these can be played using a blokus set, please add that information.
Information about polyominoes and other polyforms:
While polyomino puzzles existed long before this, Alex Randolph's Pan-Kai, from 1961 is the earliest competitive game to use the forms that I've found. Looks like it can be played with a Blokus set, or even a travel Blokus set.
1974. The description says the patterns play a part in capturing an opponents pieces, so not directly playable with a Blockus set. I only know about it after the image caught my eye during the great gallery separation project.
Also from 1977 is Skirrid, the first polyomino game that seems to break away strongly from the earlier polyomino puzzles. Plus, if the box is to be believed, you can steal away some old man's trophy wife by beating him at this game.
Super Quintillions, also from 1980, acts as either an expansion for the base game or a set of games and puzzles on its own. If you don't count the overlapping in Locus, this is the earliest 3-d game on the list, technically making it a 'polycube' game.
Cathedral, 1981. Certainly 3-D, but the color and the 2-D footprint are all that are relevant to gameplay. Has more than one single square piece per color, so this would be difficult to play with a Blokus set. Although essentially an abstract, this is the earliest polyomino game to have any sort of theme.
This Sid Sackson game involves playing tetrominoes adjacent to the last piece played by the opponent, a player may NOT use the same polyomino two turns in row, and a variation of Go rules.
R. Wayne Schmittberger's "Omino Go" also uses polyominoes (up to 4 squares) to play Go, but play is more free form: Pieces can be played anywhere. (Actually piece were made out out of 1-4 adjacent connected tiles.) The first player may play only a domino on the first turn as balancing mechanism. Otherwise standard Go rules apply. Rules can be found in New Rules for Classic Games.
This one is against the spirit of the list a little, as while each piece is a polyomino, they are all the same shape and vary only in color. Still, it appears to be an interesting game, and one that I hadn't heard of before researching for this list. 1997.