I like Battle of the Giants: Dragons for the DS. You can customize your dragon to have different attacks, appearances, abilities etc. You can even change him after the game starts. You also level him up as you progress through the fairly open-ended levels. It's a little-known game but is very good. It also comes with a starter deck for a table-top card game by the same name. The card game plays a bit like Pokemon only all the monsters are dragons. The cards look cool and the rules are easy to learn.
well, one that i play (it's a playstation game) is spyro. they have some for ps2 now. hope this helps.
~ha cha cha
but not games like how to raise a dragon or Istaria.
spyro the dragon is a great game (in my opinion)