I would second NullDevice.
If looking for a single place to begin I think the Hacking Exposed books are a great place to start. The 4th edition of the flagship book was recently released.
You can also get more specific by looking at Hacking Linux Exposed, Hacking Windows 2000 Exposed, Hacking Web Applications Exposed and Hacking J2EE and Java Exposed.
I think you can get the majority of the knowledge from the main Hacking Exposed - 4th Edition. You can also then look to the Hacker's Challenge and Hacker's Challenge 2 books to give you some scenarios to practice on.
Another EXCELLENT resource for core knowledge is Practical Unix & Internet Security (3rd edition just released recently). This book is somewhat of a bible of information security and should be required knowledge for security admins.
Outside of the stuff already mentioned, I think I would also recommend some of the stuff from Ed Skoudis. He has a book called Counter Hack and a CD-video basic hacking tutorial that will walk you through how to do some basic hacking.
It does come down to knowing your way around TCP/IP, knowing the operating system you're targeting and what services and ports are vulnerable and knowing how to program. Without that knowledge it is hard to be a hacker/cracker because without that level of knowledge you would have to rely on script-kiddie tools to do the actual attack.