Cloudflare has promised to avoid writing any querying addresses to disk and wipe logs within 24 hours. It even went so far as to have KPMG audit its code and practices on a yearly basis to publicly confirm that it's doing what it promised.
The service could speed up your internet access, too. Cloudflare has claimed that its DNS resolution is much faster than your typical internet internet provider or even rival DNS offerings, with an average of 14ms worldwide versus more than 20ms for OpenDNS and over 30ms for Google. While this won't lead to a night and day performance difference, it could make the internet feel more responsive than you've experienced in the past.
This doesn't guarantee that your info is completely secure, since DNS by its nature isn't encrypted (your ISP can still scoop up your web history if it's determined). And it's no secret that this serves as an ad for Cloudflare's performance and security services. If you're sufficiently tech-savvy to change your DNS settings, you might bring up Cloudflare the next time your employer wants to give its website a boost. Sites will see the greatest speed upgrade when they're also Cloudflare customers, to no one's surprise. Nonetheless, it's good to have an additional tool in your privacy arsenal beyond browsers and VPNs.