I know they monetize with ads and such, but I haven't found them intrusive at all. I think one of their major sources is that they have a kind of Flipboard-esque feed of news articles on your home screen at the bottom. If that is where they do their advertising then it's a model of how to do it IMO. I've found that the articles it shows are genuinely things I want to read and it's not intrusive at all; in fact I'd miss it if it was gone.
From their own FAQ: http://www.operasoftware.com/press/faq
"How Opera makes money"
Opera provides cloud-based mobile services and
solutions to operators, publishers and advertisers
and enables hundreds of millions of consumers, via
the Company's global cloud infrastructure, to
connect to the internet content and services that
matter most to them. Along those lines, Opera has
different revenue models, depending on the
customer type:
*Operators.*
Opera's revenue sources from this
hosted solution include active user fees, data
fees, NRE/development fees, hosting services,
advertising and maintenance, and support.
*Mobile consumers*
(via partnerships with search
providers and advertisers). The primary driver of
mobile consumer revenue is revenue from mobile
search, the Opera Mobile Store and active user
growth.
*Mobile publishers and advertisers.*
Revenue comes
from Opera's mobile advertising services and
technology solutions, offered to premium and
performance advertisers, ad agencies, publishers
and developers.
*Device OEMs.*
Revenue comes through license
agreements with a wide range of
consumer-electronic-device OEMs.
*Desktop consumers.*
Revenue comes primarily from
search and e-commerce partnerships.If they don't want to push me using their other services putting their hands on and selling my data, while working on secure and anonymous browser that would be really nice. Sadly I don't see there is money in a product/service like that.