I haven't been able to get in contact with any mobile phone game publishers so I'm thinking that I might try selling some of my games on ebay. Do I need to register as a business to do this for tax reasons or can it be done as a hobby thing?

You don't need to register a business, but you may need to register with the tax authority of your country and pay taxes.

You should contact your tax authority for details if, when and how to pay taxes, they'll happily provide that information.