GoDaddy certainly has a massive market share, with around the same amount of domains as the next 10 registrars combined. However, I am not sure that qualifies as a monopoly.
Just because you are a market leader, doesn't mean you are a monopoly.
They offer the same services as many other providers.
A true monopoly is a company like Verisign. They are the only company that gets to control .COM, via a sweetheart no-bid contract.
Brad