The main usage I've found for minecarts is boosting the productivity of my stone working and metalworking industries. Through clever stockpile setups and route set ups you can use wheelbarrows and minecarts in conjunction, which I'll briefly go over. I've also had some luck using it to reduce my time on the surface when getting lumber and boosting the productivity of my wood industry, but won't really get into that. There are some risks like
slamming into an obstacle and being blown apart or
colliding with minecarts. The first step to proper minecarting is setting up your piles and routes for maximum efficiency. Designate your piles right on top of the goods you want hauled out, and then set the pile to only take from linked stockpiles (press q, hover selector over pile, press a). This will prevent your dwarfs from wasting time filling up the stockpile. Next, put a stone stockpile right next to where your stop is on your route. Link the stockpiles so you are taking goods from the more distant pile and carrying them to the close one. This is mainly done to allow you to use wheelbarrows to get those heavy rocks right next to your minecart, as haulers will not use wheelbarrows to load minecarts. Careful stockpile linking also gives you full control over where your dwarfs are hauling stone from, and what type of stone.
Above is where my minecarts meet up. Its pretty crowded so it may be hard to tell even with my labels whats going on. The four tracks heading West/East all dump at a centralized location. This centeral area is designated as a stone and stockpile. Then the stockpile is linked to the workshops that require stone. Now your workers will never have to carry heavy objects far to their workshops; if the stockpile is empty the job will automatically cancel and you'll get an alert.
The track that goes North/South feeds metallic ores and economic rocks down to my magma forge layer. It is set to take only from where the E/W minecarts dump it. I haven't been able to effectively use minecarts to travel up/down Z levels, although with machines or exploits it is possible. Instead, pits still work the best for me. Just make sure you restrict the area where the stone lands as they land with tremendous force. You'll also want to keep people away from the pit in general because it makes quite a mess if this happens...
Finally, carts that are being guided are immune to collision. You can have multiple carts on the same track as long as they are being guided. It also gets rid of the risk of running over a helpless victim, at the cost of it moving at the same speed as a dwarf with a wheelbarrow. Minecarts being pushed or rode on can collide with units, but it rarely happens with traffic restrictions and alternative routes available. You'll also want to turn off hauling for your skilled laborers. For example with my set up, my masons, mechanics and metalworkers do no hauling. You won't boost your production much if your valuable workers are the ones doing the hauling.