For me, I am torn between three - Dance Dance Revolution 7th Mix: MAX 2, Time Crisis 2, and Galaxian 3.
I've been playing Dance Dance Revolution (which is too much to type, so I'm calling it DDR from here on out) since mid-2001 when I stumbled on a DDR 3rd Mix machine during a class trip to Six Flags in New Jersey. I'd already heard of the game from some friends online and it sounded both stupid and a lot of fun. If you're not familiar with the game play, the game will play a song while scrolling arrows up the monitor. When the arrows reach the top, you step on the corresponding arrow on a big pad on the ground. (Like this!) I played two or three rounds with random other people and confirmed that playing it made you look the fool, but it was also great fun. Soon after, I'd located pretty much every machine within easy driving distance and played at least weekly. When I started to progress to the higher difficulty levels, the newest version was MAX 2, which also had my favorite interface and a lot of great songs that were removed from the following release. The series still has new releases with more songs and lots of features, but MAX 2 is still my favorite. As far as actually owning one, though, they're fairly big, heavy, loud, and very apartment-unfriendly, otherwise I'd probably have found a way to squeeze one into my place. (Maybe replace that useless bed - I can sleep on the dance platform, right?)
Time Crisis 2 was the multiplayer sequel to Time Crisis 1 (imagine that). The original game was a single player light gun shooter that introduced a foot pad you would stand on to attack enemies and let go of to hide behind cover and reload. (It also had a tough-as-nails time limit that would force you to restart the current stage if you didn't play fast enough, which was abandoned for the rest of the series.) The second in the series expanded this concept to multiplayer, though unlike most light gun arcade games that restrict two players to one screen, this one gave each player their own screen and the option to play independent games or to team up and play through together. I spent a lot of time with friends at a local lasertag place going through the game over and over, and eventually was able to finish consistently on one credit. (One friend of mine could finish the game without taking damage at all!) The series has had three more games (Time Crisis 3 and 4 as well as Crisis Zone, with Time Crisis 5 coming soon) that offered extra features like multiple weapons, but for me, the gameplay of TC2 was the best of the series. Unfortunately, almost every cabinet I've seen in the last few years has one or both of the game's screens suffering major issues, and it can be hard to find ones in good condition. There's a really good home version for the PS2, though, and if you can find two copies of the game, two CRTs, two PS2 GunCons, and two older model PS2s with iLink ports (they were removed from the late-model fat PS2s and completely absent on the slim PS2s), then you can get a good home setup going.
The last one I mentioned is... well, as I said, we're assuming space, money, and availability aren't issues, right? Galaxian 3 is a shooter sequel to the original Galaxian and Galaga, both early top-down shmups where you shoot at alien invaders. Galaxian 3 differs in three major ways: First, rather than a shmup, it's a first-person perspective 3D rail shooter - you don't have control of your whole ship, just one of its guns. (Think similar to the Star Wars Trilogy arcade game that Sega put out in the 90s.) Second, while Galaxian and Galaga both supported multiplayer, it was merely alternating one at a time, while Galaxian 3 supports up to 6 players working cooperatively together. Third, Galaxian and Galaga were both standard size upright arcade cabinets, but Galaxian 3 is the SIZE OF A SMALL MOVIE THEATER. The game's "cabinet" is over 250 square feet and is literally a room that houses six chairs behind six gun turrets aimed at two huge projection screens. The game itself is designed as a cooperative experience: all players operate a gun turret on the same spaceship sharing the same life bar while shooting at the same groups of enemy ships - everyone wins or loses together. The game's visuals were very impressive at the time thanks to twin laserdiscs providing the prerendered (and therefore largely non-interactive) background with enemy ships rendered over top of the video, with audio powered by a Bose sound system. Between the huge size and $150,000 price tag, it's not a big surprise most arcades didn't pick one up. I had the privilege of playing it at Dave and Buster's near Penn's Landing a couple decades ago, and it was a lot of fun.
Though it's not something most people would ever consider getting for the home, one person in Norway DID - and documented the process over the course of six years.
Okay, enough from me - what game would YOU want? Let me know in the comments!