In HeartGold (and SoulSilver too, I expect) you can get a Mudkip, Treeco, or Torchic in addition to your Chikorita/Cyndaquil/Toyodile from the Hoenn Champion Steven. You do this by first talking to him in the Pokemon Fan Club building in Vermilion. He will tell you Latias (it may be Latios in SoulSilver, I don't know) is roaming the region. You then can speak to him in the Silph building in Saffron and he will give you one of the 3 Hoenn starters.
*I don't know if his appearence is effected at all by if you have beat all 16 leaders/Red.