Isn't there insane money to make just suing everybody in breach of gdpr? I always thought there were laywers scouring the internet in search of a quick buck.
Basically I don't think there's any money for the lawyers to pick up here.
You can.
Article 79 explicitly states that data subjects have a "right to an effective judicial remedy where he or she considers that his or her rights under this Regulation have been infringed as a result of the processing of his or her personal data in non-compliance with this Regulation.
Article 82 also states that "any person who has suffered material or non-material damage as a result of an infringement of this Regulation shall have the right to receive compensation from the controller or processor for the damage suffered."
As to the practicality of suing for violations, how would you quantify "damaged suffered" from saving a cookie in my browser?
The GDPR does not regulate cookies at all, at least unless they are a form of processing of personal data, so you wouldn't be able to sue for that.
It's the ePrivacy Directive that deals with cookies (and storing/accessing other data on your devices), and that lacks any sort of private cause of action, at least at the EU level. Directives (unlike Regulations) have to be transposed in to domestic law in EU member states, so depending on where you are there might be a private enforcement mechanism, but I doubt it.