Well, not board games exactly, because only one of them actually has a board. But they're tabletop games rather than video games, and I wanted the post title to convey that.
The first game is one I was introduced to by my friend Mark many years ago, and it is awesome. There aren't many games where four players can sit down, play for a few hours, and all lose. Wizard's Quest is a game like that. In Wizard's Quest, the deck is stacked against the players severely. You're trying to move around the board and collect treasures, but the orc horde infests the board like an ever-expanding virus. Meanwhile, you have to hope that your armies aren't killed by a rampaging dragon or the all-powerful wizard. The game gets more turns than the players do. It doesn't sound like very much fun from this description, I'm sure, but the game is a hoot. You just need to go in with the expectation that the game will likely kill all the players.
Clay-o-rama isn't a game you can walk into a hobby store and buy. The rules are available online, and all you really need is modeling clay. The game involves building your creature out of clay and then taking turns trying to destroy everyone else's creatures. Before we found the rules online, we used to play our own version, which was a bit like Calvinball in that the rules constantly changed and evolved. Our clay monsters had "hearts", and when the heart was exposed the creature is killed. Our attacks generally were butter knives thrown at the clay. What can I say? We were boys.
Medieval Economics - Perhaps the most odd and intricate of all the games here is Medieval Economics. Many years ago, we invented the rules for this game using the parts from an old Crossbows and Catapults set. I'm not sure that I can remember all the rules perfectly, since it was probably more than a decade ago when we last played, but I'll try.
We set up a system by which the plastic flags generated income. At the beginning of the game, we'd put all the game pieces in a pile, and players would take turns picking men, flags, catapults, crossbows, ammo chips, and castle blocks. Each man adjacent to a weapon could fire one shot, but ammo was limited. At the end of each round of turns, you'd receive your income and could bid on any destroyed items using ammo chips as currency. Every item in the game could be destroyed, and weapons were destroyed if knocked out of bounds.
The system we invented was remarkably balanced. Too balanced in fact - I don't think anyone ever actually won a game of Medieval Economics.