I am looking at a Godaddy dedicated server and was wondering if it is possible to run several websites from this server example.co.uk / example.com / example.net etc each website being unique and not a domain pointing / forwarding to a single website / domain?
It would depend on how resource intensive your sites become.
html/css tend to be relatively low resource usage but cms's like wordpress tend to use alot of resources.
@benandjerry like @Amadeuslopezart stated this all depends on how resource intensive your site is and the type of server you are using. I have seen some webhost state they run 300 websites per server and some may run more. You should easily be able to run your sites from a dedicated server.
I am currently using a cloud server for my websites and have 3 domains with several subdomains hosted on my server as well as other services(xmpp, irc) and the server is easily able to handle the load with plenty of resources to spare.
For reference my server has 2 vCPU and 4 Gb of Ram.