For the Dice assignment in the Game Design class at the ETC we had to design our own dice game. There were few constraints, the game had to include dice in some way while keeping in mind the balance between skill and luck. I ended up making a game I called Topple! which is a territory control strategy game for three or four players. Dice are used as much as a means of tracking board state as they are a tool for randomness. Players fill the board with dice of their color, when opposing dice enter the same square the lower valued die is subtracted from the higher die. Dice move one square at a time and they "roll" like a cube rolls. This changes what value they have facing upwards which has interesting effects on both how players attack and defend. The titular mechanic, toppling, happens when a player moves a large stack of dice; the entire stack falls over (carefully) and each individual die then engages in battle with any other dice it may land on, or restacks with friendly dice. The game was well received by all of my playtesters in a very early state and I got to spend a lot of time iterating on the smaller details to get it into a fun, polished state before submitting it.
Here's a slideshow of photos with an audio recording I took at one of my earlier playtests:
Here's another video, this time an actual video not a slideshow, but focused on the board not the players:
You can download the rules and playtest writeup here. If you have
enough d6's lying around, you can even try it out yourself. If you do, send me an email and let me know what you think!