About 6,600 according to the Mayor and cited in this Evening Standard article. But these include the bikes in storage, such bikes are not much help to people wanting to use them on the streets of the capital.
A more accurate figure, that is the number of bikes on the streets of London, that you can actually use, would be about 4900. The number (shown in the graph with the blue dots, indicating maximum values) does fluctuate a lot though:
One interesting feature on the graphs is the four red dots on their own, on the left hand side (i.e. August-December 2010) which are noticeably lower than the others. The red dots show the minimum number of bikes available (i.e. the maximum number of bikes being used) on that day. These four dots in particular, represent a four very busy day for the bike share scheme – they correspond to the four tube strike days.
Occasionally the data feed fails, for a day or so, so the maximum and minimum numbers combine. It is normally reasonable to assume that the maximum value for a particular day shows the number of bikes available on the streets, as probably fewer than 10 bikes will be being ridden at some moment during the day – the usage minimum is typically at around 4am.