Grab your digital multimeter if you want to see the world's most common use of a constant current source. The ohmmeter function for measuring resistance uses a constant current source to force an accurate, known current though the unknown resistance and then measures the IR drop created, displaying the result as a resistance reading.
A typical DMM might use a 2ma current on the 2K ohm range, 200nA on the 20K range, 20na on the 200K range, etc. A constant current source has to limit its open-circuit voltage so that it won't be dangerous. After all, trying to drive 200mA through 10K ohms would develop a lethal 2000 volts (at 200ma) and the current source would have to be capable of generating 400 watts of power.
If you know what your DMM uses for its constant current, it can be used to check the accuracy of ammeters. The DMMs constant current is likely accurate to within at least 1% even for a cheap instrument, and 0.01% for a really high-quality instrument made by by Agilent. Just connect the ammeter to the terminals of the DMM, set the DMM for it's lowest resistance range and the ammeter for a range that is compatible.
Dean