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 numeric "seed". A Seed works as a basis 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 -- as such, spawn locations will NOT look identical for identical seeds.
Seeds which cannot be parsed as integers are converted using the Java String.hashCode() function. (For instance, a seed of "abc" is converted to the numeric value 97 * 31**2 + 98 * 31 + 99 = 96354.)
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.
404 - ? Map with possible sinkholes.
21ab (1539744) - Middle of an ocean with many islands.
100 - Desert.
666 - Big desert.
87654321= Grassy patch, surrounded by snow and ice.
1234567890 - Large flat grass areas.
DIM-1 (65049612) - Large overhangs, plenty of floating islands, several 'mountains', and a large snow biome with many Pine trees.
Minecraft (-1595926131) - Snowy with a frozen ocean.
Glacier (1772835215) - lots of floating cliffs but just a cool world.
9000.1 (1677668186) - lots of floting sand and water falls
omgjizzfacelol (1460650052) - Puts you in a desert with a zombie mob spawner to your left, buried under the sand. Dig up the sand and you will find a chest with 2 bread, 3 gunpowder, 3 redstone and 1 bucket. Very Strange...
notch (105008760) - Possibly a lake with clay, and a lot of sand on the islands. Nothing really special.
Pen15 (76997853) - You spawn next to ocean and a mountain/forest with a giant overhang. At the top of the overhang you have there are some pumpkins. (x, y, z -81, 71, -59)
FinalFantasy (1201322224) - You spawn in a flatland, with hills.
291929249 - Spawns you on a map with possible stone mountains.
AssassinscreedII (-1603731033) - You spawn on an small sand island.
abcdi (92599399) - Snowy world.
gensokyo (1823221653) - Creates a very large valley bordered by well sculpted mountains with numerous dramatic cliffs, overhangs and caves. Surface lava may be nearby.
0110111101101101011001110110101001101001011110100111101001100110011000010110001101100101011011000110111101101100 - You spawn near a stone mountain (Should copy and paste seed)
mojang (-1068624430) - World with some weird cliffs.
gay rapist party - creates a desert covered with snow, surrounded by lots of frozen lakes
Several of these were donated courtesy of the thread: http://www.minecraftforum.net/viewtopic.php?f=3&t=189706