I additionally get tired of the commenters in various forums on the Internet that shoot back with the Opera being Chinese, so it must be bad. I agree with @leocg that you develop a trust with a software to feel comfortable using it. The reason why I trust Opera:
They have clearly outlined their stance when it comes to security and privacy in the links @leocg has provided.
Opera is still headquartered in Norway and therefore under European laws which are quite strict (more so then the US even) when it comes to privacy.
Opera is listed on the US Nasdaq stock exchange (ticker OPRA), and has actually done quite well over the last year even with the recent stock drop.
So my question is why wouldn't you trust the company when they clearly outline their privacy terms, they are under European laws, and lastly wouldn't want to tarnish their image which would directly hurt their stock price?
Those reasons alone are why I trust Opera and have used it for years. Users also have to remember they are a business and have to make money, so having things like Google being the default search engine, or adding features that feed their ad income is understandable, as long as those features can be disabled by the user instead of forced, which in most instances you can turn off in the Opera settings or advanced flags area if you would like.
So I am a happy Opera user, but I do hope they take the time to fix the bugs that get introduced in the newer versions, rather then rushing more new features before prior bugs are fixed. That would be my only complaint I have, but then again I understand why they have to keep the new features coming to stay relevant.