Yes, there are use of current source. One example used is for electromagnet as
[tex]\int_s \nabla \times \vec B \cdot d\vec S= \mu I[/tex]
So the magnetic flux density is controlled by the current through the electromagnet.
Driving an electromagnet with voltage source is not as accurate as the resistance of the winding can change with temperature. But using a constant current source, change of resistance only cause change of voltage across the electromagnet, the current remain constant and flux density theoretically remain constant. In most part it is true. I designed a magnetic controller using true constant current source to get accuracy into parts per million.
And yes, constant current source is used inside IC as active load. The definition of constant current source is having very high output impedance. It is used as active load for collector of BJT or drain for MOSFET in common emitter/common source stage to get maximum gain out of the stage.
I am not familiar with the latest LED light stuff, but LED is better run by constant current. If you drive LED with voltage source, you can burn the LED easily as once the LED turn on, the current increase exponentially with increase voltage across the LED. Also the LED turn on voltage change with temperature in a negative way, you can get into run off situation and burn the LED. Using constant current source, the current remain constant even the turn on voltage of the LED change.