What Should I Use My Master Ball On In Pokemon Heart Gold?

You should save it for the pokemon that flees a lot. Entei, raikou and latias will flee at the start of the battle making it irritating to catch them. If your going to try it on either mewtwo or lugia, don't. Just use dark balls, timer balls and for lugia, heavy balls.

Use it on Latias, Raiku, or Entei. Ho-oh and Lugia will be easy with a heavy ball. But seriously, don't waste it on Ho-oh. I did, and now I'm starting a new game so I don't have to live with that mistake any longer. I think Raiku would be the best though because that thing is BEAST.

Use it on a magikarp

Use it on either lotias/lotios, riakou, or entei.  The other legendarys are easy to catch with ultra balls.  That is what I did.  Now I have every legendary that you don't need an event for.  I also havent traded once

I will say raiku or entei because you can save before mewtu and lugia/ho-oh but and about latias/-os I don't know

Latias
for the non roaming pokemon:
Save before the battle so you will have inf. Chances if you ko it
bring a lot of dusk balls 3.5x catch rate at night or in a cave where as ultra balls have a 2x catch rate
catch at night
for the roaming pokemon:
Use dusk balls
whichever one is last (latias in your case), use the master ball on to get it over with

I recommend lugia or mewtwo

Mewtwo or ho-ho

Use your master ball on suicune

You should wait until you get to pewter city and get the silver wing from this guy on a hill. Then use the master ball once you find Lugia, or Use it on Mewtwo, once you beat all 16 gym badges. They are both level 70.

Moo

It is a pokeball that can catch any type of pokemon

L+r 999 masterball