Not without trading from other games. In heartgold you can get ho-oh, lugia, mewto, kyogre, and possibly celebi and jirachi through event. Others can be obtained through trading or other means. It is possible to have all legendaries on one heartgold cartridge, though, if you trade from other game. You need platinum, and emerald, and firered or leafgreen.
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Almost all pokemon with evolutions can be bred. Legendaries can not though.
the legendaries can be found when you defeated all gyms
I put a link to a guide all about legendary pokemon in HeartGold in the related links.
The cool legendaries you can get in Soulsilver/heartgold are the following: Lugia, Ho-oh, Raikou, Entei, Suicune, Articuno, Moltres, Zapdos, Mewtwo, Latias, Latios (Latios in Soulsilver & Latias in Heartgold), Kyogre, Groudon, Rayquaza (Kyogre in Heartgold, Groudon in Soulsilver & Rayquaza if you have both).
all except unow and all legendaries