picoCTF
Beginner CTF problems that are easily accessible
https://picoctf.com
Over The Wire
Bandit is an excellent beginner wargame + more wargames!
http://overthewire.org/wargames/
CTF Field Guide
Trail of Bits guide to getting started with CTFs
https://trailofbits.github.io/ctf/
Smash The Stack
Well established wargames
smashthestack.org
Exploit Exercises
Introduction and levels of Linux exploitation
https://exploit-exercises.com/
Root Me
Challenges with multiple solutions available
https://www.root-me.org
Microcorruption CTF
Scenario based CTF
https://microcorruption.com
Gracker
Psst... the source of the page is worth investigating
http://gracker.org/
pwnable.kr
Emphasizes the game aspect of wargames
http://pwnable.kr/