It has been said that a good set of tuned headers reduces restriction and can add as much as 20 HP when closed to an otherwise stock exhaust system. It is possible to get up to 40 HP with open headers.
Of course, with all other factors remaining the same, this can be further enhanced if the entire system is improved. This should include ensuring there are no restrictions in the rest of the system, i.e., head pipes (the pipes leading to the muffler(s)) and tail pipes. General tubing size is for 2 - 2 1/4 inches for engines under 351 cubic inches. It is said that 2 1/2" tubing works best for larger engines. Again, it depends on the other modifications that have been made to the engine.
Another benefit of headers is a general increase in gas mileage without sacrificing (as with some modifications) reliability. This is also one of those modifications that you can generally feel through the seat of your pants.
The only real "downer" with headers is the fact that they generally take up more space and sometime entail some fitment or spark plug changing issues. For our larger engine bays ('71 - '73 Mustangs) with the stock engines and the availability of quality headers for most of those engines, this is not too much of a problem.
Hope this helps.
BT