I think it depends on what you define evil as. There were these philosophers, and their theories of evil I find applicable to Tolkien. This is the jist of their theories, I have not read very much by them but have heard them mentioned several times and so I think this is correct, tell me if I'm wrong.
One philosopher, called Boethius and he thinks: that evil is something in man, it is internal and to get rid of it we must fight ourselves.
The other philosopher had what is called the Manacaian (sp?) theory and thought the opposite, that evil is external.
We can look at this in terms of the Ring. If evil is internal, then I do not think the Ring is a character because the evil is in ourselves (as in, in Frodo, Gollum, etc.). If evil is external, then the Ring can certainly be classified as a character or an extension of Saurons character.
I tend to think that both are true. If the Ring is a character of its own, if it is external evil, then Frodo would have had a much easier time getting to Mount Doom because he would only have to fight Sauron and the Nazgul and he could have battled the powers of the Ring without battling himself. But as we see he does battle himself, so it cannot be only the Ring that is at work here.
Sorry if this is confusing or off topic, I just thought I'd mention it. The thing I find so realisitc about Tolkien's work is this pull between internal and external evil; LotR is not a one sided fanatasy with clear-cut good guys vs. bad guys and a definate winner.