The purpose of a DNS server is to enable people and applications to lookup records in DNS tables. Most DNS servers are now private, meaning that they are configured to only provide service to the people and organizations who own and maintain them.
A few domain name servers on the Internet provide DNS resolutions for anyone who requests it of them. These are known as “Public DNS Servers.”
Most public DNS servers are public on purpose. A few public DNS servers are public only because they have been misconfigured by their system administrators. Those DNS servers tend to eventually be fixed.

Public DNS Servers
Google
8.8.8.8
8.8.4.4
Level 3 Communications (Broomfield, CO, US)
4.2.2.1
4.2.2.2
4.2.2.3
4.2.2.4
4.2.2.5
4.2.2.6
Verizon (Reston, VA, US)
151.197.0.38
151.197.0.39
151.202.0.84
151.202.0.85
151.202.0.85
151.203.0.84
151.203.0.85
199.45.32.37
199.45.32.38
199.45.32.40
199.45.32.43
GTE (Irving, TX, US)
192.76.85.133
206.124.64.1
One Connect IP (Albuquerque, NM, US)
67.138.54.100
OpenDNS (San Francisco, CA, US)
208.67.222.222
208.67.220.220
Exetel (Sydney, AU)
220.233.167.31
VRx Network Services (New York, NY, US)
199.166.31.3
SpeakEasy (Seattle, WA, US)
66.93.87.2
216.231.41.2
216.254.95.2
64.81.45.2
64.81.111.2
64.81.127.2
64.81.79.2
64.81.159.2
66.92.64.2
66.92.224.2
66.92.159.2
64.81.79.2
64.81.159.2
64.81.127.2
64.81.45.2
216.27.175.2
66.92.159.2
66.93.87.2
Sprintlink (Overland Park, KS, US)
199.2.252.10
204.97.212.10
204.117.214.10
Cisco (San Jose, CA, US)
64.102.255.44
128.107.241.185