[Neithan]

Dragons would take the Ring as a treasure as Thinlómien said. But I think that the Ring's power would work on the Dragon to some extent and it would treasure it above all other wealth. Think of what Gollom did with it and now imagine a creature who is already a treasure hoarder.
Orcs, being already evil and weak willed, would be overcome by the Ring almost immediatly. They would fade much quicker than other races.
Trolls would last an even shorter time because of their relative stupidity.
Ents would not understand a thing like the Ring. Being of nature they are wholly different from it. So I doubt the Ring would be able to corrupt them. The same goes for the Eagles.
A Valar would have no interest in the Ring but Morgoth would probably take it if he was still around. It would be far more deadly in his hands than it had been with Sauron.

As for the will of Sauron in the Ring, the ability of the Ring to awaken the desires of others is not dependent on Sauron's will. As obloguy has said the only use for the Ring is to dominate others, it cannot be used for anything else. It awakens the desire for domination in others and the desire for them to use it(the Ring) which, of course, leads to domination. This is what Tolkien was saying would happen to Gandalf, he would not become "evil" per se but he would become dominating. Just as some well intentioned religions have done.