Websites
A really awesome treasure trove of photographs from World War I from The Atlantic magazine. No matter what aspect of the war interests you, there are probably photos of it here. Seriously, they even have a section on animals in the war. It's kinda cute, it's kinda sad, and it's kinda weird.
The U.S. National Archives have the actual Zimmermann Telegram. Because of course they do; they have everything. But you don't have to travel to Washington D.C., beg them to get it out of whatever acid free dark room they keep it in, and then put on rubber gloves and try not to smudge anything. They have a website. All of the looking with none of the touching or ruining of priceless artifacts.
Books
This awesome history writer penned an engaging book about the whole affair. How's this for an opening line: "The first message of the morning watch plopped out of the pneumatic tube into the wire basket with no more premonitory rattle than usual." It's a page-tuner, even though we all know how it worked out.
Articles-and-Interviews
More information about how Room 40 cracked the code and figured out what the Zimmermann Telegram actually said. Maybe you, too, can devise a similar code and pass secret messages. Where you'll find a working telegraph office is a bigger problem.
The Library of Congress has helpfully collected newspaper articles from 1917 that mention the Zimmermann Telegram so that you can read about American's reaction to the plot as it unfolded. You get to see the actual scanned pages of the newspapers; as a bonus, you can check out what ads and cartoons looked like 100 years ago.
Video
A nice intro into what the Zimmermann note is all about and why it matters. Comes with the excellent quality World War I reenactments that one comes to expect from the History Channel, interspersed with historians saying really smart things.
Good background on the Zimmermann note focusing on the Mexican viewpoint and reaction. It includes consequences on the U.S.-Mexico border that stretch to present day, but have roots in World War I.
Images
A photo of the real deal still encoded.
A photo of the real deal translated into English.
Just in case you were wondering what Mr. Zimmermann looked like, here he is. He looks harmless enough, except for the 'stache.
The Zimmermann Telegram perfectly summed up in a political cartoon.