From an economics perspective, what are the ramifications of a currency with fixed money supply? I'm thinking specifically of bitcoins.

What are the pros and cons of having a fixed number of coins, as opposed to more "normal" currencies?  Would the currency have no inflation?
FooBar is quite right that unless you expect GDP growth to stop, fixed nominal supply currencies will lead to deflation.

A moderate degree of currency inflation serves a number of useful functions in the economy. The most obvious are:


It induces people to spend their money before it loses its value. In
a deflationary environment there is an incentive to put money under
your mattress and spend it in a year when it has greater purchasing
power. If everbody does this then the lack of demand will lead to a
decrease in overall economic activity (i.e. a recession).
It provides a weapon against downward nominal rigidities. For example, workers are generally reluctant to accept a nominal pay cut, even if market conditions are such that the current wage is above the equilibrium level. Inflation means that their employer can simply increase wages at less than the inflation rate so that the real wage is decreasing.
It erodes the real value of nominally denominated debt. Now, this is obviously only a pseudo-advantage because (whilst it benefits debtors) it harms creditors. However, this kind of erosion of debt may be desirable if national economic stability is threatened by high debt levels. Also, since debtors are usually poorer on average than creditors, it can reduce inequality, which may be a normative objective for the government.


Without inflation you miss out on these benefits. The first benefit might not seem like a big deal if you think you can simply set the rate of inflation at zero percent. But it is very hard to hold inflation constant at some target level so attempting to hit zero inflation will almost certainly result in occasional lapses into deflation, with the attendant negative economic consequences.