Q:

bound states of massless fields? 

Question: are they mathematically possible at all?  physically? 
with finite mass systems, usually the binding energy contributes to the rest-mass of the system.  It would seem that even if you could bind two massless fields/particles, the coupled system would still have a finite rest mass because of the binding energy
by any chance, is this how higgs boson gives 'mass' to particles? 

A:

Dear lurscher, a good question.  But a bound state is something that has a negative binding energy - otherwise it wouldn't be bound.  If the rest mass of a bound state AB of massless objects A,B is positive, it can clearly decay to A,B with some energy without violating any conservation law.  So AB surely can't be quite stable. 
Metastable bound states are a different issue.  I think that in some moral sense, it is true that a black hole is a bound state of gravitons, and it becomes very long-lived if it is large. 
I think it is very misleading to interpret massive particles that obtain mass from the Higgs mechanism as bound states with the Higgs boson.  The vacuum itself contains a Higgs condensate - but the individual particles such as the electron don't contain any Higgs excitations, so it is not really a bound state.  It is the original electron that has different properties because it is moving in a different environment.