I'm not sure if this is still the case, but Google used to pay them a big royalty to be the default search engine. Opera also charges a licensing fee for embedded versions such as DS lite and Windows Mobile versions of Opera Mobile and Mini.

Edit: here's the real story, from the horse's mouth: http://www.zdnet.co.uk/blogs/communication-breakdown-1000003...

And some backstory on the Google connection: http://gigaom.com/2005/09/21/google-made-opera-browser-free/