I live in the UK and have a website hosted here with a .com extension, I have also registered my site with Google. I would like to sell some products from my site to Europe, America and Australia.
Do I need to get an .eu extension for Europe etc?
Also do I have to register my site with Google Europe, Google America etc?

thanks

Google comes to you. "Registration" essentially doesn't do anything.

"Do I need..?" No, of course not. Anyone can view any TLD (Top Level Domain). Just makes it more personal if you have a domain of their type, that's all.