There's nothing inherently wrong with using other professors' exams. Sometimes profs exchange exams (as well as other teaching materials), use ones from previous years, etc., not to mention some textbook publishers issue exams to the department in a separate booklet or CD-ROM, which professors may use as they wish (meaning dozens of profs all over the country could be using it without necessarily giving credit). The one on the web may or may not even have been created by the person who posted it there.
Writing one's own exams each semester is usually preferable, though. For one thing, the exam should be tailored to what was stressed in class, which can vary, and for another, a unique exam/assignment makes it harder to cheat.
Pulling an exam from the web might be lazy and careless, but it's not likely to be taken as plagiarism. Besides, it could be taken from a textbook or some other common source, in which case the person who posted it on the web is the more irresponsible one.