Seeds are referred to the "Seeds" option when you are generating a new world. Implemented in Minecraft Beta 1.3, seeds make it so you can choose what type of world you spawn on. Minecraft players have the option at the beginning of the game to name their world, and add a "seed". This can be a series of numbers, letters, or symbols. A Seed works as a base number for a random generation of a map, in older versions when maps were randomly generated the seed was picked randomly. Using a seed should always result in the same map, but spawning locations are chosen randomly. Please note that while putting the same seed usually results in the same landforms, results may vary by system. The generation seed gives an average over the entire map, not always the exact same map.
Examples
Note: Please move to x:0 and z:0 and documenting the map from there as the spawn location differs. ?= unconfirmed
1 - A series of small islands, some which include small pools of water, and large amounts of sand/clay.
2 - Lots of stone mountains/canyons visible.
3 - Flat islands of sand.
4 - You are spawned in the middle of a desert.
5 - Flying stone cliff above water. Open air dungeon.
404 - Map with a sinkhole at the coordinates -25, 65, 15.
21ab - Middle of an ocean with many islands.
100 - Desert.
666 - Big desert.
87654321= Small grassy patch, surrounded by snow and ice.
1234567890 - Large flat grass areas.
DIM-1 - Large overhangs, plenty of floating islands, several 'mountains', and a large snow biome with many Pine trees.
Minecraft - Snowy with a frozen ocean to one side; Zombie spawner at x:-30 z:-23 y: 50
Glacier - lots of floating cliffs but just a cool world
9000.1 - lots of floting sand and water falls
omgjizzfacelol - Puts you in a desert with a zombie mob spawner to your left, buried under the sand. A chest with 2 bread, 3 gunpowder, 3 redstone and 1 bucket nearby. Very Strange...
notch - Some clay, a little lake that may lead out to the ocean, and a lot of sand on the islands. Nothing really special.
Pen15 - You spawn next to ocean and a mountain/forest. If you climb up the mountain towards the side you will find a giant overhang with monsters inside. At the top of the overhang there are pumpkins.
FinalFantasy - You spawn near some caves, large mountains, and a flatland in the middle. There is also a pumpkin sitting on a cliff.
0110111101101101011001110110101001101001011110100111101001100110011000010110001101100101011011000110111101101100 - Spawns you on a map, look behind you, theres a stone mountain. (Should copy and paste)
AssassinscreedII - You spawn on an small sand island, find the dungeon. (Coordinates: -12, 59, 1)
Several of these were donated courtesy of the thread: http://www.minecraftforum.net/viewtopic.php?f=3&t=189706