Hackthissite - http://www.hackthissite.org
A nice site (even though it has been having problems recently) including basic web challenges, "realistic" missions, basic cracking and encryption challenges.

ngsec - http://www.ngsec.com
A great website, with some tough final challenges. Including SQL Injection and some Buffer overflow challenges.

Try2Hack - - http://www.try2hack.nl
One of the most well known hacking challenge sites, its levels are basic and ideal for those new to security.

Hackerslab - http://www.hackerslab.org
A great site with levels based around unix security, you'll either want to use linux or have a copy of putty to complete any of these challenges.

SlyFX - http://www.slyfx.com
A great challenge site, starts off with some basic maths and moves onto solving application problems (starts with some basic debugging and moves onto solving stuff)

Mod-X - http://www.mod-x.co.uk
Never completed this site, got a little bored with it. But on the whole rather good, if you've played the game uplink it's that sort of story (i think, as I said, never really played it I got bored at lvl3 )

HackMe @ Elderson - http://hackme.elderson.net
Only a few challenges, but they are interesting ones.