If you want a proper wargame, get Conflict of Heroes: Awakening the Bear. I've just gotten into it and it's fantastic. It involves moving chits on a hex map, but they're one inch square linen-textured chits and the maps are gorgeous. Each time you play it you will play a "Firefight", which is their term for mission. There are two player missions, and also four player missions. More are available for download on their web site. Most are aimed at two players, though, so a regular four player group will be replaying the missions over again (I think there are four such missions available, but of course they're really big and there's a lot of variation).
One thing that is cool about it is that there are no charts to look up. You're rolling 2d6 plus the unit's firepower rating versus the other unit's defense rating (it has two, depending on if you are hitting it from the front or not). Firepower values labeled in red go best against red defense, but are halved against blue defense... and the same with blue firepower ratings (red being anti-personnel and blue being anti-tank). So rather than have a special rule for gun shields, shielded guns just have a front blue defense and a flank red defense. It's all pretty simple and elegant like that. If you hit the enemy unit, you draw a damage chit. It is killed if you hit by four or more, draw the killed chit, or if it is hit while already under a damage chit. Also, the way it does "overwatch" and the fluid nature of the battlefield is that for every action a unit executes (move one space, firing, trying to rally, etc.), the opponent may declare a reaction move right after that (so if you move, I can fire at you, then you can move again, etc.). You take turns activating units so there is a lot of back-and-forth. Good game, and fast. Oh, it's about Operation Barbarossa, by the way.
Another wargame that supports multiple players is Memoir '44. You have to buy two sets, though, or buy the special Overlord boxed expansion... but if you do that, you'll have to settle for using cardboard counters for some of the units rather than M44's premier feature, the little plastic dudes. There's even a special expansion aimed at playing "Overlord" style called "Hedgerow Hell", which is obviously about Normandy. It's a good game but there's a fair bit of luck involved, because you only get to move your battalions using cards. If you don't draw good cards, you're going to sit there getting owned and not be able to fight back very well. But it's fast and usually fun. Nota Bene: a famous boardgame reviewer seemed to think that playing the game in "Overlord" mode refers to the fact that each side has one top general which he called the "overlord". Obviously, it actually refers to Operation Overlord, which was the name for the invasion of Normandy by the Allies.
Risk 2210 suffers from being Risk, which is to say that it's obviously highly stylized. You move "armies" into whole countries/regions and I'm not sure what it all represents. However, in this particular version you get to conquer the Moon, and I'm can't think of why any reasonable person wouldn't want to do that.
