Well, notice that Peach is the only roalty ever referred to in the Mario Bros. franchise (exept for a very inconvincing king in SMB3), So I'm left to infer that Peach is the sole ruler of the mushroom kingdom. I think Bowser kidnaps her so he can "have his way" with her, but not sexually. I think when Bowser kidnaps Peach, he makes demands, and he'll keep her captive until she promises to meet those demands. But, being the noble empress she is, Peach refuses, to say, make an altar and sacrifice 3 virgin toads to him every week. So she stays captive, for the rest of her life if she has to. Which she doesn't, because Mario shows up in a week or two to kick some arse.
Although, I think Bowser's recent plots have been out of spite for Mario, because, frankly, if I got whupped repeatedly by a pudgy italian plumber, I'd be pretty mad too.