<p>I'm writing a client-server app using BSD sockets.  It needs to run in the background, continuously transferring data, but cannot hog the bandwidth of the network interface from normal use.  Depending on the speed of the interface, I need to throttle this connection to a certain max transfer rate.</p>

<p>What is the best way to achieve this, programmatically?</p>

The problem with sleeping a constant amount of 1 second after each transfer is that you will have choppy network performance.
Let BandwidthMaxThreshold be the desired bandwidth threshold.
Let TransferRate be the current transfer rate of the connection.
Then...
If you detect your TransferRate > BandwidthMaxThreshold then you do a SleepTime =  1 + SleepTime * 1.02 (increase sleep time by 2%)
Before or after each network operation do a 
Sleep(SleepTime)
If you detect your TransferRate is a lot lower than your BandwidthMaxThreshold you can decrease your SleepTime.  Alternatively you could just decay/decrease your SleepTime over time always.  Eventually your SleepTime will reach 0 again.
Instead of an increase of 2% you could also do an increase by a larger amount linearly of the difference between TransferRate - BandwidthMaxThreshold.
This solution is good, because you will have no sleeps if the user's network is already not as high as you would like.