Flashgot

This lets you pick a "download manager" to use for downloading links and images. You can highlight an image and right click and download the selection (which can includes images and/or text). You can do the same after right-clicking a link.

The good part is that you can use any arbitrary program as a download manager. So you can write your own script that downloads the image to a folder of your choosing and immediately opens it in a program of your choosing.

You can also drag-and-drop an image from Firefox into some programs directly. Or drag-and-drop to a file manager window (e.g. your desktop) depending on what OS you use.