In addition to the efforts going on in Ottumwa, there is the already-existing American Classic Arcade Museum, located inside Funspot in New Hampshire. This arcade was prominently featured in the cult-favorite documentary The King of Kong: A Fistful of Quarters. I don't think their mission is to collect every single game ever (that would be a lot of them) but they sure have a huge collection of both popular and obscure games.
The museum is really just one floor of the arcade (there are three) featuring many, many classic arcade games in excellent working order. I imagine the maintenance is a perpetual nightmare, but they do what they can. There is no admission fee, just ordinary tokens to play the games. Most still cost one token (each token costs a quarter, or less if you buy in bulk), and let me tell you $20 goes a long, long way there. For maximum childhood regression, they keep the lights down and play awesome 80s tunes over the sound system. I was there a couple months ago and got to play some games that I had not laid hands on for a long time: Elevator Action (last played at Fuddrucker's), Missile Command (pediatric dentist's office), Sinistar (Lamppost Pizza), Dragon's Lair (Chuck-E-Cheese), Star Wars (basement of the local Sears), Tapper (local bowling alley), Crystal Castles (by the front door of the local Alpha Beta supermarket) and so on. A few machines I had never seen before in person (a stand-up Pong machine, Satan's Hollow). They even have a friggin' Computer Space, but alas it was broken when I visited. The fact that you're even allowed to touch it is amazing.
I also got to play the infamous Donkey Kong machine, where I was proud to hold the high score (a piddly 18,000) for probably five minutes, and the same Pac Man machine where Billy Mitchell played the world's first perfect game of Pac Man (I think I cleared about 3 boards).
It's a real experience - if you're in the area I highly recommend stopping in.