In New Horizons, there are 6 breakable tools (in several strengths), several unbreakable ones, and a wide variety of wands. You can find out how to get the golden variations here.
Tool durability is complicated - see the section below for more details.
|Flimsy axe||40 uses|
|Golden axe||200 uses||
|Stone axe||100 uses|
|Worn axe||3 uses||
|Fishing Rods||Colorful fishing rod||30 uses||
|Fish fishing rod||30 uses||
|Fishing rod||30 uses|
|Flimsy fishing rod||9.5 uses||
|Golden rod||90 uses|
|Outdoorsy fishing rod||30 uses||
|Nets||Colorful net||30 uses||
|Flimsy net||10 uses||
|Golden net||90 uses|
|Outdoorsy net||30 uses||
|Star net||30 uses||
|Shovels||Colorful shovel||100 uses||
|Flimsy shovel||40 uses||
|Golden shovel||200 uses|
|Outdoorsy shovel||100 uses||
|Printed-design shovel||100 uses||
|Slingshots||Colorful slingshot||20 uses||
|Golden slingshot||60 uses|
|Outdoorsy slingshot||20 uses||
|Watering Cans||Colorful watering can||60 uses||
|Elephant watering can||60 uses||
|Flimsy watering can||20 uses||
|Golden watering can||180 uses|
|Outdoorsy watering can||60 uses||
|Watering can||60 uses|
|Nook Inc. uchiwa fan||∞||
|Party popper||Single use||
|Bunny Day wand||∞|
Tools have a fixed durability, which is reduced by usage. When a tool reaches zero, it breaks. The rules for durability loss vary by tool:
Axe: Lose durability when hitting rocks or trees, or fruit-smashing rocks. Do not lose durability when hitting other items, players or missing. Axes at 1 durability will not break when hitting a rock that gives an item, or when fruit-smashing rocks.
Fishing Rod: Lose durability after successfully catching a fish/rock/egg/whatever. Do not lose durability when failing to cast or catch.
Net: Lose durability after successfully catching a bug/petal/whatever. Do not lose durability when failing to catch.
Shovel: Lose durability when hitting rocks, or digging things up. Do not lose durability when burying things, filling in holes, or hitting non-rocks. Shovels at 1 durability will not break when hitting a rock that gives an item, when fruit-smashing rocks, or when fruit-digging a tree.
Slingshot: Lose durability when popping balloons. Do not lose durability when missing.
Watering Can: Lose durability when watering unwatered flowers, or watering the ground. Only 1 point of durability is lost, regardless of the number of flowers watered. When watering the ground, only 1/20 of a point of durability is lost. Do not lose durability when watering already-watered flowers.
For tool variations that allow it, customizing a tool resets its durability. If you get your timing right, this makes for cheaper tools than crafting/buying new ones.