After beating Red, you can catch Groudon. If you have caught him and trade for a Kyogre you can also catch Reyquaza.
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It's not the "last" Legendary Pokemon that you can find in Pokemon HeartGold, but most people usually catch that one last given that you need to have both Kyogre and Groudon in your party for Professor Oak to give you the Jade Orb to get to Rayquaza.
In the pewter city museum. to get his attantion you must bring walking latias ( heartgold) or latios ( soulsilver ) with a soul dew from a mystery gift. then he will take you to saffron city. he will talk to you for a while. then he will go back to pewter then show you latios ( heartgold ) or latias ( soulsilver ) outside of the museum. then after you defeat or catch one of eon Pokemon that's the last of him.
Houndoom is not considered a legendary pokemon because it is easy to get multiple houndooms. Legendaries are generally pokemon that can only be caught once in any given game (and are also difficult to catch as well as usually among the last pokemon in the pokedex for a region).
GET THE LAST BADGE......
You can catch one of the three legendary dogs; Bulbasaur=Entei, Squirtle=Raikou, Charmander=Suicune. you can catch them in vermilion city, fly to vermilion city and go north, you can find them in the last rows of grasses in the upper part of vermilion,