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 )
The originally definition of a hacker was a talented computer programmer that could solve almost any problem very quickly, often by innovative, unconventional means. Today it is sometimes used to mean someone that tries to break into other people's computers or creates a computer virus, which isn't quite as noble a concept -- these folks are more properly called "crackers". The following sections provide descriptions of various famous Internet hackers and crackers and provides references to a few well-known hacker related sites.