.co.uk is the country code for United Kingdom. The .co portion of the extension indicates the domain name is for commercial purposes (similar to a standard .com extension). It is unrestricted and may be registered by anyone, from any country.
.org.uk is the country code for United Kingdom. The .org portion of the extension indicates the domain name is for an organization. It is unrestricted and may be registered by anyone, from any country.
.me.uk is the country code for United Kingdom. The .me portion of the extension indicates the domain name is for an individual. It is unrestricted and may be registered by anyone, from any country.
All UK domains don't have .co.uk tacked on the end. It depends on what the domain will be used for.
Edit: Here's a list of the rest:
UK TLDs - .uk Top-Level Domain Divisions
.co.uk Commercial
.org.uk Non-Commercial Organisations
.ltd.uk Limited Companies
.plc.uk Public Limited Companies
.ac.uk Academic
.gov.uk Government
.lea.sch.uk Schools
.mod.uk Ministry of Defence
.nhs.uk National Health Service
.net.uk Networks
It's pretty much the same deal for other countries.
Here is some more info if you're interested.