As others have posted, there are two basic considerations: fire danger restrictions and environmentally based restriction. These are imposed from without.
I'd like to raise the idea of a third consideration: what is ethical backpacking practice? In other words, even in areas where there are no mandated restrictions, I would still ask, "is this a place where it would be a sustainable, very low impact practice to have a fire?"
For me, I've pretty much come to the conclusion that at or near tree line, in thinly treed areas where wood is scare, or in overused areas, I won't have a fire even if there are no restrictions against it. Generally, I won't have a fire above 10,000' in the Sierra, rules or no rules. Since a lot of my trips in the Sierra have camps above 10k, a wood burning stove isn't typically what I carry.
Having said that, I have no problem with burning wood in areas where wood is plentiful and the impact of fire is very low. There are plenty of highly worthwhile coastal and front range trips where one will be camping below 10k for which a wood burning stove, absent fire restrictions, would be great. Call me old fashioned, but I sure do like having a wood fire. :)
I've had to wrestle with this issue a bit. When I started hiking, camping, etc. in the 60's, we always used wood, which was a common practice. I don't think I ever used a BP'ing stove until the late 70's. At first I resented the imposition of fire bans but later realized that it's not 1968 anymore and that burning downed wood does have an impact on the health of the places I love to hike.
OK, so long post :) but those are my thoughts FWIW.