Let’s take a break from the Dominion-centric Tabletop Tuesday. People who are interested are probably already reading Dominion-specific sites. Dominion is on one extreme of a continuum in that every player starts with exactly the same resources and options. Some games like Risk or StarCraft give everyone the same option pool to start but then provide different starting points, or different victory conditions like Illuminati.
At the opposite extreme you have games that offer asymmetric options: vastly different starting resources, methods of playing, rules, and/or victory conditions. Balance here is difficult to do well, especially since a playstyle that works well for one side may not work at all for another, but a successful asymmetric game is a really great experience with multiple experiences built in.
The simplest way to do this is have asymmetrical forces fighting each other. Ogre is a classic example: one giant tank versus many tiny soldiers and vehicles. Dino Wars! is a similar idea, pitting plastic dinosaurs against little green army men. The old Netrunner CCG and its reincarnation as Android: Netrunner also feature a monolithic corporation against a more nimble runner. These seem to be the standard ways of dividing the teams: big vs. small and/or defense vs. offense.
The other popular version is to have one side be the heroes and the other the monsters. This takes the classic Dungeons and Dragons Dungeonmaster role and makes it explicitly adversarial, with finite resources on both sides. Descent is one of the most literal takes on that, with a party of heroes against one person representing the dungeon. Last Night on Earth plays out zombie apocalypse scenarios with humans vs. zombies, something like the Left 4 Dead versus mode with the zombie side controlling the horde rather than having special undead. Betrayal at House on the Hill starts all the players together then switches one of them to controlling the enemies when they are revealed.
I am rather fond of differing victory conditions, because it gives the game a feel other than the standard “destroy your foes” or “have the highest score.” Shadow Hunters is a tabletop game that gives you a mix of both: there are two opposed factions trying to destroy each other, and those characters may have alternate victory conditions, and there are neutral characters who have their own victory conditions that may or may not align with either faction. Just because you died does not mean you lost; your team may yet win or the surviving characters might complete your victory conditions.
I also support multiple victory conditions. I love the feel of Civilization, where we might be racing on different tracks as I try to build the perfect society while you try to conquer the world and Ethic is trying to colonize other worlds. I also love that you could have a faction of mad cultists who win through sacrifices to the blood god on the same board as a faction of faeries who win if the cards in play complete the color spectrum. Illuminati gets special credit for having a shared victory condition plus a unique condition for each faction.