Browsers opens only https sites I have OS X Mavericks on my Mac and 3 browsers (Firefox, Safari, Chrome). 
When I try to open any site I see only "connecting..", but when I try https sites it works fine!
Ping and traceroute shows normal information.
Internet works over Wi-Fi. (My iPad works fine and opens any address).

I have tried to restatart mDNSResponder and turn off Firewall. But my problem still persists.

Any ideas?
188.43.69.98 is a Russian IP and announced as owned by 'Closed Joint Stock Company TransTeleCom' and not is not an official Google IP.  It tries to disguise itself by falsifying its reverse dns pointer pretending to be 'cache.google.com' but this is a lie.

Chances are very high your system has been hijacked somehow.  Perhaps not your Mac but your internet router could be compromised.  My guess you have an ADSL connection on a TP-Link or D-Link ADSL router which are easy targets.

Log in into your router and check what the DNS servers are set to.