DNS 1.1.1.1

A promising DNS resolver with a security and privacy focus is the new free offer from Cloudflare ​called 1.1.1.1. While DNSSEC ensures integrity of data between a resolver and an authoritative server, it does not protect the privacy of the "last mile" towards you. DNS resolver, 1.1.1.1, supports both emerging DNS privacy standards - DNS-over-TLS, and DNS-over-HTTPS, which both provide last mile encryption to keep your DNS queries private and free from tampering. The DNS resolver, 1.1.1.1, is also supporting privacy-enabled TLS queries on port 853 (DNS over TLS), so we can keep queries hidden from snooping networks. https://1.1.1.1/

Other DNS resolvers include:

Google Public DNS: Google is doing a great service for the world with this free DNS resolution service. This will speed up your browsing, improve your security, and get you results with no redirection. But guess what? They get something out of it too. They get data. Their DNS resolver is at the address 8.8.8.8.
  
Quad9: In association with the Global Cyber Alliance and Packet Clearing House and a consortium of industry and non-profit contributors, Quad9 provides a DNS service designed with privacy and security in mind. This reduces risk, speeds browsing, and since it is being fielded by a non-profit there is no collection of personally identifiable information like some other providers. DNS address is 9.9.9.9.

Verisign: Verisign Public DNS is a free DNS service that offers improved DNS stability and security over other alternatives. Verisign respects privacy. DNS data and other PII is not sold or shared or used to serve you ads. Their DNS address is 64.6.64.6