As a general rule, it’s a good idea to keep images as small as possible because loading large images will slow a site down. However, they should never be uploaded with a smaller size, in pixels, than the size at which they will be displayed. For example, if an image is 600px wide but it is enlarged to stretch across the full width of the screen then it will look terrible.
The difficulty is that you need to balance “as small as possible” with your desire to display high quality images and you should take into account the purpose of the image. It will be important that the images in a photographer’s portfolio look fantastic, but if all you are doing is using a picture of a sundial to illustrate a blog post on time managment, then you may not be so fussy.