I've noticed on a few sites I've been on they say if you need to go any further you must allow cookies.
Looked at this site
and it looks like that they can take your info and do what they like with it.

You have to do something on your pc to disable cookies - not opt in to accepting them.
Are they a good or bad thing (becoming a backdoor into your pc?)

This explains it well:

http://en.wikipedia.org/wiki/HTTP_cookie

The majority of cookies are harmless, used to hold you're login info for a site, for example, but some are used to track activity and are used to target advertising.

As far as them being used as a back-door to access your computer, there's nothing to worry about.

If you want your browser to remove any saved cookies when you exit, there should be a setting to do exactly that. The setting to do this is in different places depending on what browser you are using. Do a Google search for the relevant info and you'll find exactly how to do it.

As above, but remember, if you set your browser to clear cookies on exit you will need to manually login to every site (that requires it) that you visit, even if you have visited it before.

They at most keep your preferences, it more in your face if you live in Europe and the UK as its Brussels again.
We have our own Notices

https://www.wikiwirral.co.uk/cookies/

You can turn off your Cookies Derek but you cant log in with out them, well you can but every page refresh you would be logged out.

At wiki you can click on My Stuff and then clear cookies.
That will remove cookies from ""YOUR"" computer not ours.
We dont store your cookies there stored on which ever device your using, laptop phone or computer.

Cookies are stored on your computer.
Cookies are harmless.

We all have to give in to them to enjoy the internet the way we do. It sounds scary but its only since March or May last year it became law, but the word was it would be so hard to police and it would be so much of a pain no one would bother. But the Big Players started to roll it out a year later and we have all started to follow suit.

If you were in the states you would not see any of the warnings, as its only the EU and UK users that need to see the warnings.

Hope that helps.