There is already a thread about minecart science, but its mostly about how to weaponize them. I want to discuss ways to use them to improve your efficiency.
Automatic quantum stockpiles:
The simplest one is the automatic quantum stockpile. Have the first route stop accept loose items from an input stockpile. Then, at the last route stop, build a track stop set to dump to an adjacent tile. Designate a 1x1 stockpile that accepts all of the items being dumped onto it so dwarves won't haul them back to the start as this would create an infinite loop. Try not to have the items fall down one or more Z-level or they could cause injuries.
Express highway:
Normally, you should have your carts set to be guided instead of pushed or ridden. Not only does this prevent accidents, dwarves will find their way to the correct stop even in a complex network of interweaving tracks. However, you can setup a highway track if the path is linear there are no pedestrian traffic crossings. Create an intermediate stop along your route set to push or ride in the same direction the cart was moving. At the end of the highway, build a track stop construction with high friction and switch back to guide mode.
Farm Delivery:
Create a food stockpile next to your surface farm that only accept outdoor plants. Do the same for the underground farms but set them to only accept underground plants. Build tracks that connect both to a central repository. Have the initial stops load up plants and have the last stops dump them into a quantum stockpile. You can further divide up what plant goes where by setting up track lines for each type of plant with their own destinations.
Automatic used clothing cleaner:
Create a finished goods stockpile that accepts only clothing and enable refuse, but turn off all refuse options. Let this stockpile take from anywhere. All loose clothing will be hauled here and disentegrate.
How to protect your replacement clothes from it:
Set up a finished goods stockpile that only accepts items from links. Tell this stockpile to take from your clothier workshops.
Please post any other discoveries.