CloudFlare is a f.ing nightmare for anonymity
Not only anonymity, but privacy as well.
Try browsing around with your browser's Referer header disabled (or spoofed to be empty/google/etc). You'll run into sites that either (1) won't load at all, only showing a "CloudFlare security page" that totally blocks access, or (2) have content that won't load due to CloudFlare's default referrer blocking settings. I assume (2) is to prevent "hotlinking" (aka - "using the Web"), but it prevents scripts, styles, etc from loading. However the first behavior (blocking anyone without a Referer header) is complete bullshit.
Using NoScript on a CloudFlare site can also be a nightmare. They have their own absolutely batshit absurd scripting thing call Rocket Loader. The only impression I've gotten from it so far is that it makes script whitelisting difficult and user-scripts even worse.
I can appreciate the primary selling points of CloudFlare (CDN, DDoS protection), but they do a lot more to interfere with site web traffic. The default settings for a site are also probably too aggressive.