Active filter with series inductor and resistor - do these exist?
Inductors are generally more expensive, more bulky and less ideal than capacitors so you'll usually see a strong preference for capacitors over inductors. Only very tiny values can be put into an IC, whereas useful values of capacitors can be integrated.  

However, series inductance is frequently used where conductors enter a shielded enclosure or signals enter a PCB. Sometimes as inductors, sometimes as ferrite beads (which are inductive over a range of frequencies) and sometimes as common-mode chokes.