I've got a rusty old downpipe on my external brick wall that needs replacing, however the bolts on the brackets don't seem to have useful heads.
See photo: https://docs.google.com/file/d/0B0HOZkGABny5a01DdEZmUkNXS2c/preview
Any idea how I would get these out without ruining the wall?
I got a look at the picture finally. The bolts are drive pins, and the bracket has a slot that will allow the bracket to slide off to the side if you can get one removed I would guess. The bracket looks pretty thick, whereas, if you ground one of the heads off with a small right angle grinder that would allow the other side to slide off from the side. Then use vise grips to grab the head of the pin and rotate the pin, that should work it loose to remove it. If that works then do the same to the other side you ground off. But this wild be the way I would do it if the first try doesn't work.
First thing I would try is vibration. Tap the pin like you are trying to drive it in more, since it will not, it will vibrate. Vibration is the bane of masonry fasteners. If the pin is set directly into the masonry, this may release its hold.
What I also see in the picture is a larger hole that the pin goes into. This perhaps is filled with a wooden dowel then the pin is driven into that, forcing the dowel to split, or "grow" so to speak, grabbing the diameter of the hole harder so the pin will not withdraw. If this is the case, grip the head of the pin and pull out with a slight twisting motion. It may help to have a prybar with a fine edge, almost chisel like, to start under the head of the pin to help ease the pin out. Again, if it is a wood dowel inserted into the larger hole under the bracket. You may be able to check that by tapping a slim nail into the slot of the bracket, into the hole in the brick and see if it hits something hard or soft. Hard bad, soft good. If soft, you may be able to simply pry it all off with the same prybar I mentioned before.
Cut the heads off using a reciprocating saw. If you do it correctly, the bracket will prevent the blade from damaging the wall.
If there's enough to grab hold of you could try using a pair of locking pliers and unscrewing them. The benefit is that you may not have to drill new holes for a new bracket. You could also try to pry the bracket off with a crowbar. If the screws are rusted out enough the whole assembly may come out in one piece, along with their mounting plugs. Don't put too much pressure on though, you don't want to damage your wall! Put a then piece of wood or plastic between the fulcrum of the crowbar and the wall to prevent any marks as well.
If neither of these works saw them off as @longneck says.
