Here are the game design resources that I've personally found most useful in my new day job. (Now I know where to go when I need to re-order something!)
Bits and Prototyping Materials
I buy nearly all my wooden bits from spielmaterial.de. They're a bit expensive and shipping from Germany takes awhile, but their selection and quality is hard to beat. They're my go-to for standard Euro-game fare: wooden cubes, pawns, meeples, and disks, among other things.
I buy more cribbage pegs than I ever thought reasonable from Casey's Wood Products. They also carry the usual craft line of unpainted blocks, beads, balls, eggs, golf tees, checkers, and so on. I picked up the buttons and spools for the Knit Wit prototypes from them.
After many years of experimentation I've found that card sleeves work the best for me for card prototyping purposes. I can print on regular paper stock, letting me iterate quickly. Plus, the sleeves come in a variety of colors and (perhaps most importantly) they're reusable. I've been buying UltraPro sleeves at full retail price – if anyone has a good source for sleeves in bulk, let me know in the comments.
For 3D components, I do a lot of rough prototyping in craft foam. Read more about this magical prototyping material in my article, Craft Foam: the Poor Man's 3D Printer. I've been doing a lot of laser cutting lately, but still find that sticker paper + craft foam makes a fast, cheap, first pass.
I find inkjet-friendly sticker paper indispensable and buy it in bulk from Label Outfitters. It's not as opaque as the nicer Avery version, but it's a lot cheaper. The letter-sized sheets can be had for less than 10 cents a sheet in bulk. Sticker sheets let you "print" on essentially anything whether it's foam, chipboard, wooden bits, dice, or your prototype box.
If you're looking for inexpensive boxes to store and carry your prototypes, Paper Mart is my favorite. Their tab-lock tuck-top mailing boxes work well for many games. If you have smaller games, they have a flip-top box with a magnetic closure that's pretty swank.
Books
Of all the books on game design that I've read, the one that I found most useful is The Art of Game Design by Jesse Schell. The author approaches the craft through 100 different "lenses" or perspectives. These lenses are also available in a card format that I highly recommend.
Raph Koster's A Theory of Fun thoughtfully explores where the fun in games comes from. Koster embellishes nearly every spread with playful illustrations that help communicate his points.
Edit: 16 March 2022. Looking at this with fresh eyes, some parts of the book could use an update: the section on gender presents some problematic framing and is best read critically.
Rules of Play by Katie Salen Tekinbaş and Eric Zimmerman is the textbook of game design and reads as one. This book is chock full of definitions and dry descriptions of the many elements involved in game design. While I found it interesting academically, I didn't find much in it that I could apply directly to my process.
One of the best ways to increase engagement in your game is to find ways to modulate your players emotions. This concept is explored in depth via "beat analysis" in Robin Laws' book, Hamlet's Hit Points. Laws describes a vocabulary of up and down beats, describes how they can be used for better storytelling and role playing, and deconstructs three stories using them to get you fully acquainted with the vocabulary.
Software
I use a pretty lean software kit these days and can do nearly everything I need to accomplish with Adobe Illustrator (prototype illustration), Google Drive (journaling, data tracking, playtest logs, punch lists, file sharing). Illustrator's a pain-in-the ass to learn and use, but after nearly (gulp) 30 years of use, I find it indispensible.
I use Skype and Sococo for communication, avoiding email as much as possible for sharing information that exceeds more than a few sentences. I favor Drive (for asynchronous stuff) since it synchronizes with other contributors and offers full history, and Sococo (for realtime communications) since it offers voice, video, chat, screen sharing and rich presence info.
Tools
I burned through a bunch of low-grade paper cutters before finding the Dahle 507 Personal Rolling Trimmer. If you need accuracy, it'll split a .5pt line (if you're cutting one page at a time). If not, you can cut up to about 8 pages of 20lb. stock in one go. Do yourself a favor and get a great cutter.
Blogs and Podcasts
Cardboard Edison compiles useful articles on game design from around the web. I found their industry reports particularly interesting.
I'm not an avid podcast listener or player of roleplaying games, but if I were, I'd be devoted to Ken and Robin Talk About Stuff. As it is, I pop in occasionally and always leave impressed with how literate, articulate, and just plain smart the hosts are about story construction and a whole host of other topics often tangentially related to board game design.
And if you're not following Board Game News on BoardGameGeek, you're missing out on what's happening on the scene. W. Eric Martin's been on the beat for years now and really knows the industry and the players.
Am I missing out on something truly great here? Let me know in the comments.