Will regular money still work when we begin to build outside of earth. Its believable that someday, we may be able to live elsewhere. We definitely will have to if we are to survive as long as the universe is. Will the US Dollar continue to work across planets or space stations. My guess is we will begin to use a digital currency. Some systems are already in the making.
The two most popular are:
Bitcoins are a currency that are being mined by solving hard problems with extra computing power. There is a finite amount and mining should in about 100 years or so. The faster these things are mined, then the harder they are to receive. The price of bitcoins recently went to 200 US dollars per coin and dropped suddenly. At the time of this post, the price hovers around $100 a coin. A very volatile investment and is open to corruption but still a decentralized form of trade. It is anonymous and avoids fees that banks use so it has become popular with less than legal forms of trade.
Recently, new hardware has come out from butterfly labs that blows the old stuff away. Of course this means the complexity of the problems your hardware is given to solve will become extremely difficult and lower the amount of bitcoins you can get overall. You would almost have to have a large business mining bitcoins to make it profitable for you when these start rolling out full scale(more on this: Jumping in to Bitcoin Mining).
Litecoins are another viable alternative. These are similar to bitcoin and can be mined effectively with the GPU (video card) and processor you probably have already. You can even convert bitcoins and litecoins between each other for another form of currency trade. Which will win or will both succeed and fail? We will have to see.
No specialized hardware has been made specifically for litecoins as they are not as popular as bitcoins. Mining can still be done on a personal level. Like bitcoin there is only a finite amount, so mining faster yields a higher complexity and less coins for everyone. This could change someday and when it does, i would buy the equipment asap and be the first to raise that complexity.
The best part of trading with these digital currencies is that there is still money to be made. Even though they are 100 bucks a coin, you can still buy and sell with small fractions. The market is extremely volatile and experimental but the coins have been holding value. There are many places to trade the coins for services and goods. My favorite is where you exchange bitcoins for gold. You can obviously make more trading on mtgox but if the market begins to fall, trading in for gold may be a good idea fast.
Money that is all digital would be ideal in a space environment. It can be instantly transferred and holds value. If we could trade money in space, a non-physical currency may be necessary. Maybe the US government will jump on board and start making a digital version of the dollar. Time will tell.