Our company has implemented a photo cropper in an ASP.Net MVC application using Atalasoft's DotImage. I did not implement this myself, but I currently maintain the whole of that application (and consequently the cropping component).
Based on the way you phrased your question, I feel that I should explicitly point out that Atalasoft's DotImage only provided the functionality to manipulate images. Other answers referenced ImageMagick and GDI+. In the same vein, these libraries also only provide the functionality to manipulate images.
We had to implement the UI and workflow ourselves. This was, while not rocket science, still far from trivial. While we used a pre-built component for fancy, AJAX-y file uploads (for the source photos) - we still had to integrate that into the application and manage persistence of the files and database records associated with them. (Similarly, as a convenience we allow import photo from url - another feature we had to explicitly create)
I would suggest that you will not find any general purpose component to integrate that will give you cropping functionality and a Web UI. I suppose there may be one made by a ASP.Net component vendor, but I am certainly not aware of any off-hand.
The problem tends to involve lots of pieces that span from the client to the server, and consequently I think what you are looking for will involve a fair amount of specific-to-your-application development and integration.