The well known interest rate parity relationship from international
finance is as follows:
          F = S * exp[(r-rf)T]
where 'F' is the forward price in dollars of one unit of foreign
currency, 'S' is the spot price in dollars of one unit of the foreign
currency, 'r' is the domestic risk-free interest rate, 'rf' is the
foreign risk-free interest rate, and 'T' is the time.

According to this equation, if the foreign risk-free rate is higher
than the domestic risk-free rate, the foreign currency weakens
relative to the domestic currency. However, if the risk-free rate in
the foreign country is higher than the domestic free rate, investments
held in that country will earn a higher rate of return. Therefore,
money and investments should tend to flow in the foreign country,
driving up the value of the currency, rather than weakening it. Could
someone make sense out of this paradox?

The paradox arises because the equation you specify is only part of
the model, specifying a quasi-arbitrage relationship.  There is an
implicit assumption here that flows of investment between the two
countries don't themselves effect the exchange rate (this is not as
bizarre a model as one might think; there might be a central bank
policy to this effect for example).

When you add a money market equilibrium condition you have the guts of
Dornbusch's "overshooting" model.  The idea is that, because (in order
to maintain interest parity), the currency of the country with the
lower interest rate has to be expected to appreciate over the period
T'-T.  But as you correctly note, a higher interest rate would
normally attract inflows of investment which would have the effect of
moving the exchange rate in the opposite direction.

This can only be made consistent if a fall in the domestic interest
rate leads to an immediate step fall in the domestic currency, so that
it has "room" to appreciate; this is the solution of a model with two
equations, one of which is the one you set out above and the other of
which is the money market equilibrium condition.

There is a good explanation here:

http://mahalanobis.twoday.net/stories/1418105/