(When) do people use Nydus worm?

Nydus worm can be very effective in many different use cases.

Combat: All you need for a nydus worm deployment is line of sight which you can easily achieve with an overlord/overseer. This can be an effective way to get through a walled in opponent without actually taking out their wall. Nydus worms also generate creep so you could even setup spine crawlers if you so wish.

Another way to use it in combat is to distract your opponent. Because the nydus worm can be heard anywhere, they usually go into panic mode and will send their army back to their base or will be otherwise distracted in scouting for it at which point you can attack with your army without actually using the worm.

Its also important to note that when a nydus worm node is destroyed the units inside are unharmed unlike a warp prism, medivac, overlord. Unless you take out the whole network.

Economy:

This is a bit tricky and requires you to be on top of things micro wise. But you can use a nydus worm to mine out an undefended high yield without actually building a hatchery there.

Setup the nydus worm in your base right next to your hatchery and set the rally point to your hatchery then shift click back to the node. Then where you've opened the nydus worm at the high yield, set its rally point to the minerals then back to the worm.

Hot key your nydus worm's mineral node to a key and the base node to a key. Load it up with a bunch of drones then every 20 seconds (i forget the exact timing) select the opposing nydus node hotkey and press 'D'. this will unload your drones, and depending on which side they unloaded they will either start mining or they will return the goods back to your hatchery.

Obviously this use is very complex and requires you to remember to unload and at which node to unload at (have the drones just mined or just returned gathered minerals?). You also lose the added benefit of having more larva and another hatchery.

1v1 is risky at this point in time because of the time it takes to build and the noise it makes. It is also easily killed.

However, in team games, a nydus can be very effective which is where I personally will use it. It is an agreed upon strat with my teammates, usually someone's observer provides the line of sight. I've used it to get a quick mineral line attack when the opponents push out, and I've also used it to provide a smaller secondary attack to draw attention away from the main forces of my allies while they attack.

The main uses have been posted, but another use is simply as an intra-base tram system. On big maps, it can be very handy to shuttle armies around very quickly using the Nydus network. You can even use it to ship your attacking army up to the frontlines, and send in reinforcements quickly like how Protoss use Warp Gates.

Another use is expansion defense. If you are a good little Zerg and have lots of expansions, you can save resources on defenders by simply adding a Nydus worm exit or two to each expansion. Then you can keep a few dozen Hydralisks in the system, and pop them out if they are needed. It's not as good as static defenses since the units exit one at a time, but it can help protect isolated expansions.