A cookie is a text-file. That means it cannot be executed. It can only be created, read and modified by a site and that's all done by the browser on the site's request. A site can only interact with (create, read or modify) its own cookies. So cookies are quite innocent then and won't breach my privacy?
Here's an example. I have a Facebook account and I usually don't click on advertizements. However a few weeks ago I did click on an advertizement in Facebook that I hadn't seen before. The click took me to the site of a well-established online-shop. Nothing sinister about that. However, since that click I've been seeing that same advertizement on Facebook, but also on some other favorite sites. That could only have happened by means of a global cookie. I don't quite like that, because it means someone can follow my web-surfing habits.
But what if you, as user, don't accept cookies at all? Sorry, doesn't work. A lot of sites wouldn't function without them and consequently you couldn't use them, so you need cookies. Removing them after every browsing session is a hassle, but it should help. Removing cookies when you switch from one site to another would probably make it difficult to follow you. However removing all cookies means you would have to give up convenience. E.g. you would become an unknown user for every site and would have to enter your login credentials at every visit to the sites where you have a login and need to login.
There's no viable or user friendly cure other than changed rules. Global cookies would have to be outlawed or somehow made impossible.