A few months ago, Cloudflare revealed their public DNS server, and I’ve been pleased so far. In addition to performance, Cloudflare claims to be investing heavily in security of DNS. The top competitors in this field already being Cisco’s OpenDNS and Google. As these are all global players, they will (in most cases) have better speed and reliability than those of your local ISP.
Changing these for your entire network generally involves the administrative features/config of your gateway, modem or router. If you are familiar with this, the change should take just a minute or two.
If you are looking for some content filtering at the DNS level, OpenDNS still presents the easiest option for home users and also provides logs.
Google Public DNS: