As this thread has shown there are many possible reasons for using an anhedral tailplane (and that also applies to just about any aircraft feature you like to consider). I think most of the tailplane ones have been mentioned. There can be structural reasons as well, for example if you would like the tailplane mounted lower for an aerodynamic reason but it is not so easy to arrange the structure to mount it at that height then bend it down. (The Hawk was a bit like that as it had to go above or below the jet pipe - in the middle would have been a very heavy solution structurally).
Also never forget the difference between dihedral angle and dihedral effect. What we need as drivers is just the right amount of dihedral effect (ie the right amount of roll due to rudder or rolling moment due to sideslip as the aero guy would say). Getting that is not just a matter of wing dihedral angle. A tall fin and rudder will have its centre of lift well above the fuselage (about 1/3 up the height would be a reasonable assumption) so in this case left rudder produces right roll. Then there is the matter of the height of the CG with respect to the wing – high wing with low CG gives left roll with left rudder. Sweep back produces relatively huge amounts of left roll with left rudder. In this context an anhedral tailplane gives right roll with left rudder as does wing anhedral.
Sooo, it is often the case that things having a large dihedral effect are chosen for reasons other than lateral stability (sweepback and a high wing being two obvious ones) This means the designer will have to fiddle with all the elements that have individual dihedral effects in order to optimise the overall AIRCRAFT dihedral effect. If you get it wrong to start with then the dihedral angle of the tailplane will probably be easier to change than most of the other things.
JF