Minecarts are rideable objects placed on minecart tracks that are used to carry items, move the player faster, move automatically over a long distance, and to ride roller coasters.
Minecarts can be destroyed and reverted to a carriable item, even while riding them.
Minecart Riding
The old rideable minecart.
Basic Physics
Minecarts can be ridden by right-clicking them, but the player cannot move the minecart while inside of it so it must already be in motion when sat in for it to go anywhere.
The minecart physics have been noted to be very unrealistic. Once pushed downhill a minecart will gain speed at an increasing rate until it reaches a cap. It also moves significantly faster/farther when ridden by a player rather than when pushed empty. An example of this is riding a minecart after being pushed up/down a slope of one block after which it will travel around an amazing 78 blocks, though very slowly by the end. A player can rapidly re-enter the cart or add "boosters" on tracks to increase speed.
Players riding minecarts are not able to move, but they can exit the minecart by right clicking it. It is also possible to interact with the environment while riding a cart, such as shooting a bow at enemies or laying down track in front of the minecart while it is moving.
After rolling off of a track, a minecart can be pushed around on open blocks.
When riding a falling minecart, landing will deal no damage.
A minecart will stop when it encounters a dropped item.
If an animal is hit or pushed into a rideable minecart, they will ride it. They will escape if the player right clicks to ride it themselves (pushing out the animal) or if the cart is destroyed. They may also exit it after a while.
Energy Conservation
A chicken riding a cart.
Although the minecart has a maximum speed, it does not appear to have a maximum energy. One can create a slope upwards of a tested 60 blocks, and achieve further and further travel distances.
One unit of energy could be defined as the energy gained by a cart going down a one block slope, and lost by a cart when it goes up a one block slope. If a 45 degree downward slope is connected directly into an upward slope, an initial height of 60 blocks will result in a final height of 40 blocks, a loss of 20 units of energy. But if 20 sections of flat track are inserted between the slopes, the final height will be 35. This implies that one unit of energy is lost for every 4 sections of horizontal track traveled with an initial stored energy of between 60 and 40. At much lower speeds, much less energy is lost, implying that the energy lost is a percentage of the cart's current energy. The above gives about 0.5% energy loss per section of track. One implication of this is that more energy lost when the cart has more energy, so a gradual slope should allow you to travel much farther distances than a steep slope followed by a long flat section.
Anything in the way of the minecart will take it to a dead stop, including: blocks, items, mobs, and moving off of minecart tracks. When a mob touches a minecart they affect it in the same way a player would, i.e. minecarts in motion bounce away from mobs in the way of its motion and mobs that move up against a still cart will set it in motion.
Animals now seem to be able to ride in mine carts as well allowing for transportation.
Boosters
Minecarts can act very strangely when their next to each other, this effect can be used to create boosters. The booster consists of a second (much shorter track) with another minecart, the two tracks will have one or more squares of contact. When your minecart gets next to the other the game glitches and gives both carts maximum speed and also infinite energy, meaning nothing will be able to slow them down (except a full stop). This is very glitchy however and sometimes minecarts will disappear because of this. Example of longer contact, example of single-square of contact.
Powered Minecarts
A cart that goes forward by using fuel, see Powered Minecart
Storage Minecarts
On Friday July 30, 2010 Notch added storage Minecarts, along with powered Minecarts. To create a storage Minecart, simply craft a Chest one block above a Minecart. These Minecarts can be accessed by right-clicking. After destroying a storage Minecart you will receive a Chest and Regular Minecart block. To recreate the Storage Minecart simply press 'i' to open your inventory and place the Chest above the Minecart in the crafting section as you did earlier.
Some notable trivia is that minecarts with storage or furnaces are the first crafted item created from two separate crafted items, and that minecarts were originally storage only, and did not require a chest.
Minecart Trains
After Friday July 30th's Minecart update, creating Minecart trains became a much simpler solution to transporting goods. To create a Train you should start with a fairly short length of straight track with an open ending on one side. Put the Powered Minecart on the side nearest the open end, and then add Storage Minecarts or Ride-able Minecarts along the rest of the track. Then turn on your Powered Minecart and watch it push the other Minecarts as if it were a Minecart Train! Placing another Powered Minecart on the other end will allow you to make a two-way train, as minecarts currently only push other carts, not pull.