Inflationary (no total coin limit) cryptocurrency where miners keep all new coins
PPCoin and its offspring NovaCoin have an infinite money supply - even though the reward for blocks gets diminished over time (as in Bitcoin et al.), as the money supply increases there will be more and more coins offered as reward for simply hoarding the coin.

There are also built-in deflationary mechanisms for destroying coins with every transaction, so hopefully the money-supply would self-adjust: increasing or expanding as needed, depending on how much it's actually used.