Blokus seems like it will be near the top of the list of abstracts any grandkids I have will be playing. In addition to being a very good game, it seems to have broken out of the gamer niche and made it to the mainstream audience.
The original Blokus is a pure abstract for two-to-four players, although it does four the best by far. The games comes with a big, silver 20x20 board of slotted squares and four sets of 21-pieces in different colors. The pieces are every possible combination of shapes made of of squares from one square to five squares and are slotted to fit in the grooves. They're also transparent so they look extra groovy.
The players take turns putting one piece down at a time, starting from the corners. The twist is that every piece after the first one _must_ touch the corner of another piece of the same color _but_ cannot touch the side of a piece of the same color.
The game ends when no one can place any more pieces. Your score is the total number of squares you've covered. What that really comes down to is counting all the squares on the pieces you haven't been able to play with the low count winning.
Blokus is the not the first game that's been all about putting down geometric shapes in a board. Alexander Randolph created Universe in the 60s, which uses two sets of Pentominos (all the combinations of five squares). Cathedral from 1978 is another one that comes to mind and I bet there are tons shape placement games I've never heard of.
So what makes Blokis special? The groovy silver board and transparent pieces? Actually, what I think it comes down to is Blokus actually has the simplest rules. Touch corners, no touch sides, no capturing rules. Everything that goes on the board stays on the board.
At the same time, while 400 spaces is a lot of room to work with. There is a lot of replay value in Blokus, not to mention a lot of patterns to explore. Even with the basic strategy of use your biggest pieces early and move towards the center that the game really requires, there is so much to explore.
Personally, I actually prefer Travel Blokus (redesigned for two players only) and Blokus Trigon (which uses shapes made out of triangles) but neither of those games would have been possible without the original Blokus. It is a simple game but it's found its way out into the world and had impact.