I have heard that the maximum block size means that the Bitcoin network has a maximum throughput. What is this maximum?
The current block size limit is 1MB, but this is likely to be changed in the future.
Transactions are about 500B, so the current limit is 2000 transactions per block, or about 3 per second.
From the Scalability on the wiki page
Today the Bitcoin network is restricted to a sustained rate of 7 tps by some artificial limits. These were put in place to stop people from ballooning the size of the block chain before the network and community was ready for it. Once those limits are lifted, the maximum transaction rate will go up significantly.
There's also some charts comparing to other payment networks