I'm with Ard on this one. Absolutely a situational question. I'll break off dead branches to get my flies back (though this is situational too... depends how much the frustration has built up
). For me, I'd rather leave the overhanging branches that sit close to the water and protect the holes, but the branches over my head that are already dead yet still groping for my flies, they are open season if they are on those waterways that already get heavy pressure (read: those streams that serve as yearly battlegrounds for combat fishermen).