Though I have an innate fear of sites leaving their cookies on my computer, the truth is that I haven't had any NOTICEABLE difficulties because of them. They make it a lot easier to sign in to a site where I'm registered (like entering DaniWeb without having to sign in with my name and password each time) and they seem to store information about business deals that I have started but not managed to complete in one visit.
The warnings I have heard about programs that study your store of cookies and then start badgering you with ads or pop-ups based on your internet preferences has never shown up on my computer (at least, I haven't noticed it). But this could be to the credit of my anti-virus/anti-spyware program.