Basically, MVC serves well when you have an application that needs separation of the data(model), the data crunching(controller), and the presentation of the data(view). This also serves well in an application where the data source and/or data presentation can change at any time. So the data can be coming from a DB, RSS feed, twitter API, etc and can be presented in an RSS feed, normal XHTML, an mobile version, etc. By seperating the app into the three layers, you can develop for all these different scenarios by simply creating a corresponding view or model.
Most of the time, a web site/application seams to somewhat naturally fit into this pattern; partly also because of the popularity of the pattern as of late, some just use it without thinking.
I don't really think this is a direct answer to "when is it not a good idea." I would say when you application doesn't naturally/easily seam to fit the idea. If you have to really shove it into the idea, start changing/adding/deleting things to get it to work as a MVC, then it isn't time for it. Remember that the MVC is a design pattern, so it is a possible solution to a specific circumstance. There are other design patterns for other circumstances that might suit your application better. Here is a link to some good articles introducting design patterns, and then going to some of the basic ones.