Although I have the quick links on the right side, I thought I'd try to give more information about the links.
When it comes to puzzle shops, you're only going to find a link here if either I've used the shop/store personally myself and have had no negative experiences, or someone who I know and trust has used them and their recommendation is that the shop is good to deal with. I've been fortunate in that I've not had any bad experiences with puzzle stores. Mostly they're run by puzzlers, and the puzzle community is a really good one. I've made many good friends though the puzzle community, and have no doubt I'll make many more!
Hopefully you find the information here useful.
All the best, Neil
Creative Crafthouse is a small family business, who makes their puzzles in house. The site offers a large array of puzzle designs, including Puzzle Boxes, Tavern Puzzles, Disentanglement Puzzles and many more. They even carry some unique designs that only they make, so definitely worth having a look. They ship worldwide, so no matter where you are, ordering is possible.
Puzzle Box World
Puzzle box world is a family run business specialising in Puzzle boxes from around the world. they have an excellent selection, and are very nice to deal with. I've used them several times for a number of purchases and never had any issues. They also have a Facebook page where they often post discount codes or special offers, so I'd suggest keeping an eye there for some good deals. They ship worldwide, so no matter where you are, you can order from their site.
Puzzle Master is a Canadian manufacturer of Wire and Disentanglement puzzles. They now carry a huge selection of mechanical puzzles and toys and work with a number of distributors to bring you some superb puzzles at very reasonable prices. They are also increasing their own puzzle line, which are designed and built by themselves. I use Puzzle master frequently, and highly recommend them. The team there are great to deal with, and tend to get your orders out pretty quickly. I have found a number of puzzles available at Puzzle Master that you can't get anywhere else. In the interest of full disclosure, I am a Puzzle Master affiliate, and do make a small amount of money for traffic sent to them.
Puzzle Paradise is an online Puzzle Auction site. You'll find a lot of rare and high quality puzzles here, and while the puzzles may not come cheap, you're likely to see puzzles here that you may not see anywhere else. Many of the puzzle world's elite designers and puzzle builders will auction spare puzzles from their production runs here. Always worth keeping an eye on.
Revomaze is the puzzle that got me back into puzzling again recently. They make the highest quality metal and plastic hidden maze puzzles that I have seen. These puzzles are not cheap, but you do get what you pay for. The current series of puzzles increase in difficulty from Blue, Green, Bronze, Silver and the soon to be release Gold. Dealing with the company is a pleasure. I have personally talked with the creator and owner, Chris Pitt a number of times, and he's a great guy. Customer service and quality are high in his mind, and he goes out of his way to make sure that things are right with his puzzles. If you're looking for a different challenge, you would do well to look here. Revomaze also hosts a forum for their puzzles here. There are many like minded people over there, and a lot of information on other puzzles too. Worth a visit even just to find out more about the Revomaze craze.
Wood Wonders is run by Brian Menold from a small basement workshop where he makes hand crafted wooden puzzles normally just a few at a time. His puzzles have a unique, sometimes, one-of-a-kind quality as a result. Made from domestic and imported hardwoods, they are hand sanded and hand waxed. No stains are used. Only the natural wood gives our puzzles their rich warm appearance. I have purchased puzzles from Brian, and he is a great person to deal with. Currently a donation from any sales from his puzzles is being made to Breast Cancer research as Brian and his wife recently lost their oldest daughter to cancer. My best wishes are with him and his family.
Vin&Co is the site of Vaclav Obsivac, otherwise known as Vinco. He is a superb craftsman, and makes some stunning wooden puzzles, mostly co-ordinate motion puzzles, but all of superb quality, with very good tolerances between pieces. Given his large selection of co-ordinate motion puzzles, Vinco is known in the puzzle community as the master of co-ordinate motion. Vinco's puzzles can be found on many puzzle stores, however I have dealt directly with Vaclav, and he's a great person to talk to and buy from. Shipping is very reasonable, and he'll make any puzzle from his collection for you on request. It may take a week or two depending on his workload, but you'll end up with a beautiful puzzle in your hands. Highly recommend his puzzles, and buying directly.