These are the ice tools that I have used and recommend. Most of these products are used/shown in The Ice Book. Most of these links go to Amazon.
If you're coming to this page fresh, you'll want to check out the Index of Ice Experiments here on Alcademics.
Clear Ice Cube Trays
There are now a lot of trays that make ice without hacking! I think the Clearly Frozen tray gives you a lot of bang for your buck.
For spheres, I like the Dexas Iceology tray. It's well-built and the ice pulls out more easily than with any other tray. It makes slightly smaller spheres than I would like. The brand's square 2-inch cube trays are also excellent. I recommend Dexas products to people more than anything else.
Another great product is the Ghost Ice Compact System. It's super heavy duty and makes 12 cubes at a time.
Three-Prong: Most of the time I just use a 3-pronged ice pick for cutting up blocks of ice. Several manufacturers make the same model. I have one by Fortune Candy. This is another one of the same style.
I have used this more popular and less expensive three-pronged pick, but mine quickly rusted.
Single-Prong: I rarely use a single-prong ice pick, favoring the three-prong one in nearly all situations. I do have the Anvil Ice Pick and it's well-made.
Cooler to Make Clear Ice
I use the Igloo Island Breeze 9 pretty much every day. It took about 8 years before I accidentally froze it solid too many times and had to replace it.
I have not used the Igloo Legend 6 but it's a little smaller if you have less room in your freezer.
DIY Ice Cube Trays using this method
Ice cube trays - Any of the large 2-inch silicone ones from Tovolo, CocktailKingdom, etc.
Drip Irrigation Standard Tubing Hole Punch ($6)
Clear Ice Balls and Death Stars Using a Thermos
The links for the ice ball molds keep changing so make sure to double check, but for now here is one that looks like what I buy. Just be sure to buy 2.5" ones that are separate rather than stuck together in a 4-pack.
I have also made Death Star ice balls using this mold.
Small Ice Balls
For Larger Programs - Bars and Events
The Ghost Ice Tray fits into a large Coleman Party Stacker cooler and can fit in a walk-in freezer and some chest freezers. It makes 48 2-3-inch cubes in about 2 days. I tried out a smaller version here but it's really priced to use in the bigger cooler. The big system seems built to last - ultra thick silicone.