Each planet will have its own locally-mined cryptocurrency (Marscoin, etc), which each have a floating exchange rate to the original Earth-based Bitcoin. Marscoins and bitcoins can be directly traded for each other in order to settle interplanetary trade balances, the only issue is the speed-of-light delay for confirmations (which is unavoidable no matter what). Naturally Bitcoin can't be mined on Mars and Marscoin can't be mined on Earth, but that's not important.
An interplanetary coin with a block target of several Earth days (to allow interplanetary mining) is also a possibility for interplanetary trade or as a solar-system-wide reserve currency, but probably not necessary as long as the planetary coins can be freely traded, in which case it's likely that Bitcoin will become the solar-system-wide reserve currency (making all previous price predictions seem hopelessly pessimistic).
That pretty much nails it.
Does anyone remember The Probability Broach by L Neil Smith, wherein space faring humans in an alternate universe use gold and silver coins as currency? And the use of fingerprinting techniques is seen as revolutionary in forensics investigations?
Also, does the topic of currency ever come up in Ursula K. Leguins The Dispossessed?
And Charles Stross in Neptunes Brood:
https://bitcointalk.org/index.php?topic=252633.0Also: on Orionsarm:
http://www.orionsarm.com/forum/showthread.php?tid=302"...it's divided into slow, medium and fast money. Fast is every day cash, medium is investments in infrastructure and slow is money that can only be transferred once the sender, receiver and a bank have all registered the trade. The point of the latter is that all three will be in three separate systems and because of how long it will take to organise slow money payments will be immune to problems of inflation and financial fraud that cash would be over interstellar distances.
Hmmm. One of these sounds a bit like our favorite coin, doesn't it?