My sister also sent me a link to a problems website run by the Harvard Chemistry and Chemical Biology Departments.
A databank of good and interesting problems is a great idea. (I don't know much about chemistry, but my sister claims that these are good problems.) Just as it is hard to find good textbooks, it is difficult to find good problems -- they should do this for every quantitative subject. There is the additional problem of cheating, but that's another topic...
Aside #1: I think that most students can tell the difference between the professor who is giving them random problems from the book and the professor who genuinely wants them to learn and only assigns problems that he/she would actually be willing to do. If students actually enjoy doing the problems (at least after solving them) and the problems tie in well with the course, then you have a successful class.
Aside #2: I used to think that my teachers brilliantly came up with their own problems, but I quickly learned that. For example, one of my best undergrad classes was the second and third semester of the quantum mechanics sequence. It turns out that one heroic and brilliant professor developed all the course materials and they get used over and over again (though sometimes people add a little something new). As my high school English teacher told me, the best teachers "steal."