Well it may be a good idea to explain what cookies are before we start. First of all, there are two kinds of cookie:
1. Server Side Cookies
Server side cookies are snippets of information about you which are stored on the web server that hosts the website. Each time you view a web page you are sending information about which operating system you use, which web browser you are surfing with, even what your screen size is among many other things. They can also hold personal information about you if you fill out a form. You don't have to worry about companies getting your name and address as long as you don't fill them in on forms. If you don't do this then they can't know the information.
In summary, it is an easy way to temporarily store information (which can then be used to be stored long-term) about your visit to a website. They can save nothing that you don't want to give them with the exception of things like your screen size and browser etc.
2. Client Side Cookies
These are the cookies that are often talked about in public circles and can be the source of much paranoia. Client side cookies are snippets of information about you that are stored on your own PC. Depending upon which browser you use, they will be stored in a folder somewhere in your computer. They can be there for one minute, one hour, one month or anywhere up to 25 years!
What happens is that the website you are viewing can decide to save these bits of information about you so that they can be re-used when you go back to the website. Fror example, you may have bought something in the past and when you sign back in there is a part of the website which says "Welcome John...". They are able to do this because they kept a copy of your name on your computer.
OK that's fine, but should I be worred about cookies on my computer?
In my opinion no you shouldn't. The first reason is that one website cannot access a cookie created by another website (there is an exception to this explained below). In other words, they can only access information that you gave to them in the first place.
The second reason is that it is very easy for you to delete cookies on a regular basis. This may inconvenience you in part because they can do some very useful and helpful things. But if you are worried about cookies this should alleviate your fears. I do not recommend blocking cookies as this can cause many useful modern websites not to work.
The exception to the rule
I said earlier that no website can access cookie information saved by another website. Whilst this is strictly true, there is a sneaky way that some companies get round this. Let us say that abc.com and 123.com both use the services of def.com. abc.com can ask def.com to store the cookie on your computer and give back all information held for themselves as well as for 123.com. This could work for any company using the services of def.com. This might be illegal and may not happen that much, but it is a potentially small risk.
In my view, as long as you deal only with reputable companies you have nothing to fear and if you are still worried, then set your browser to delete all cookies on exit.