I don't see a completely-free Opera browser in its future, but when you look at it, in the advertiser-supported version:
The ads are not intrusive, they are up on the toolbar - out of the way of the rest of the browser screen.
Lately, I have noticed ads from some larger entities as well as colleges and universities. So if Opera can attract organizations of that caliber, then Opera is clearly doing something right.
UserAgent: Opera/7.11 (Linux 2.4.20-4GB i586; U) [en]