Photoshop equivalent software (for free) that can remove part of a picture?

I have a logo and I want to remove the background colour in it so it will fit into a colour scheme on a brochure I am designing. Essentially I want the background colour on my logo to become just void space (not plain white) until I paste onto my brochure. I know you could do this on photoshop but its expensive. Any free alternatives that can do that task? Thanks all.