Server

Minecraft servers allow players to play online with other people. They may either be run on a dedicated server, or be temporary, and run off a home machine.

How to make a server
For help with port forwarding, portforward.com is a good source, alternatively one can read the documentation supplied with the router, modem or other ISP related hardware.

If all else fails, the official Minecraft forums have users with information on hosting servers.

Following this guide might also help you:

Connecting to your local server
Once your server is up, you start sending the external URL to your friends. If you have trouble logging in through the external URL, you can use the local IP to join yourself, make sure you're logged in and use the following URL:

http://cprogramminglanguage.net/

If you changed the port in the configuration file you'll have to change that in the URL too.

If someone in the same network wants to connect to your server, that person will have to use the same link, but change the IP address to the hosts local IP address.

You might have trouble connecting to your own server while others can join without problems. This can be solved by changing "verify-names=true" to "verify-names=false" in the server.properties file.

Types of servers
There are numerous kinds of Minecraft servers, usually distinguished by the level used in them or how players in them are supposed to behave. Many special types of servers rely on the use of map editors.

Standard
Standard servers usually have relatively regular maps, allowing players to build or destroy whatever they want (though griefing is often against servers' rules).

Falling lava
A form of roleplay, falling lava servers usually use a small map with a single block of lava or a lava "timer" (a long channel through which lava flows, delaying its spread) at the top of it. Players are intended to try to construct a shelter so as to "survive" before the lava engulfs the map; the map usually reset/restored sometime afterwords. Some maps use water in the place of lava to make building after the flood easier.

Roleplay
A server, usually with a normal map, where players are encouraged to take on roles and act as them in the game. These servers often attempt to simulate settlement in some foreign land or similar, and require the gathering of resources to build structures.

Spleef
Spleef servers are usually dedicated to playing Spleef. They use a nonstandard map which contains Spleef arenas, of which are generally much more extravagant than those a standard server might have.

Grief
Though rare, a grief server usually consists of another server's map which the grief server's owner would retrieve, therefore allowing people to "grief" without getting banned.

Randomly-generated
A map design generated using either the standard in-game generator or an external generator such as Omen. While the in-game generator can only create temperate-themed maps, desert-, mountain-, hell-, snow-themed maps and others can be created with external generators.

Flat
An otherwise standard design which is not randomly generated, but is instead simply a vast grassy plain. These are usually created by various external generators.

Ocean
Ocean maps usually consist of mostly or entirely water to encourage building underwater structures; they may also be dry at first, but flooded later, after players have built on them. These gained more prominence when sponges were added.

Cave
A server which is mostly or entirely an elaborate cave or series of caves, far more spacious and dynamic than standard caves. These commonly have the top and sides blocked off with admincrete to stop light getting through.

Landscape
Landscape server with widely varying features across the map, such as caves, forests, mountains and oceans. These are commonly custom-made and used in roleplay.