I’ve taken to using Kagi. It may not meet your privacy requirements (more below), but it does keep the web wonderfully shopping mall free. It’s a paid search engine, it sources results anonymously from other search engines as well as its having its own internal database. I generally find because the search results are weighted by its own criteria which in no way is influenced by ad revenue decisions they tend to be pretty good – plus you can customize them by assigning your own weightings to sources you like to use a lot (like, say, Wikipedia) or ones you never want to see (like AI-generated spam domains). Privacy may be where it breaks down for you, and will depend on your threat model. For the most part, my privacy concerns are more for private businesses and advertisers – which it excels at protecting me again. If I was concerned about law-enforcement it may be less desirable (it is run out of the USA and is presumably subject to subpoena), likewise for state-level espionage (and if that’s your concern, you wouldn’t be asking this question anyway).

All in all, hugely happy with it and totally think I’ve gotten my money’s worth from it – but I also totally get a lot of people aren’t interested or are unable to pay for a search engine. I figure I’m paying one way or another, and I’d far rather pay this way than with my time sorting through ad spam. If you are interested, they have a tonne of documentation explaining their philosophy, search results, privacy policy, and what all you get for your money.