Possible? Yes. (Search on "screen scraping")
Easy? Can be anything from moderately easy if you know something about server-side programming, to annoyingly difficult if the target web site's structure is malformed and inconsistent.
Ethical/Legal? Lots of possibilities there, from no big deal (maybe they'd be happy to sign an agreement with you to get the free advertising) to you better hope they don't notice and call their lawyers.