Yes, and fairly easy, as I recall. You can even selectively re- or de-colorize bits of an image, if you're somewhat skilled with layers and have access to the original. There's several tutorials out there as guides, and here are some from GIMP.org, the main site for the GIMP project.
This one is interesting, in that this one will let you selectively colorize certain parts of an image you've previously decolorized, so that you can create images that look like the art photos you often see that are primarily black and white, but are partially colored.
For such simple tasks, the GIMP is completely over-qualified.
I can highly recommend IrfanView for the most simple image editing (size changes, cropping, greyscale conversion, or converting images to different types).
The quickest way is to open your photo, choose Colors on the menu, then Desaturate. It will give you three options (Lightness, Luminosity, Average) - choose the one that looks best to you.