How many world seeds are in Minecraft?

There are 18,446,744,073,709,551,616 (2⁶⁴) possible seeds. All seeds are a number, if letters are entered into the seed box, Java's hashCode() function is used to turn it into a number.

Seeds do not use up much disk space (stored as a long integer, meaning just 8 bytes per world) because only a seed that has been chosen for a world is stored; not all 18 quintillion. When a seed is needed for world generation, a random one is generated from the system clock (or entered manually by the user) and is then stored and used to generate the world.

How many possible worlds can generate, including customization options? Probably more than any computer can calculate given all of the float sliders available in a customized world.

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Here's an image showing a randomly generated seed:

-3,010,441,696,458,036,422 is far lower than both -2,147,483,648 and -140,737,488,355,328. This means that seeds use higher than 32 bit and 48 bit signed integer ranges.

I originally stated that Minecraft uses Java's default Random class for pseudo-random number generation. Random uses 48-bit seeds.

However, that would imply that the seeds 1 and 2⁴⁸+1 result in the same world, which others have pointed out is not true. So I did some more digging.

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Minecraft appears to use Random everywhere except for the biome-generation code. There, it uses its own homespun random generator. From GenLayer.java:

protected int nextInt(int upperBound)
{
    int randVal = (int)((this.chunkSeed >> 24) % (long)upperBound);

    if (randVal < 0)
    {
        randVal += upperBound;
    }

    this.chunkSeed *= this.chunkSeed * 6364136223846793005L + 1442695040888963407L;
    this.chunkSeed += this.worldGenSeed;
    return randVal;
}

This is a linear congruential generator with values a = 6364136223846793005 and m = 1442695040888963407. This will indeed produce 2⁶⁴ distinct output streams, and thus there are 2⁶⁴ distinct worlds.

The claim on the Minecraft wiki that "Multiplayer seeds may only have 2⁴⁸ possible values [..] due to using Random.nextLong()" is incorrect. The single-player and multiplayer world generators are not different.

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The use of Random everywhere else does mean that some things will be the same between seeds that are off by 2⁴⁸, such as seeds 1 and 2⁴⁸+1. For example, the location of ores should be almost the same between the two (except for ores removed by cave-systems).

Also, the use of per-chunk seeds has some interesting consequences. For example, given the small number of biomes and the large number of chunks, in any given world there is a very high probability that there are two chunks which are exactly the same. Finding those chunks, however, involves math which is beyond me. If anyone is interested in figuring it out, the code for initializing the chunkSeed is

public void initChunkSeed(long chunkX, long chunkY)
{
    this.chunkSeed = this.worldGenSeed;
    for(int i = 0; i < 2; i++)
    {
        this.chunkSeed *= this.chunkSeed * 6364136223846793005L + 1442695040888963407L;
        this.chunkSeed += chunkX;
        this.chunkSeed *= this.chunkSeed * 6364136223846793005L + 1442695040888963407L;
        this.chunkSeed += chunkY;
    }
}

So the answer is found here: http://minecraft.gamepedia.com/Seed_(level_generation)

Which even though it's already linked on this page no one seems to have read it all.

To summarize:

If you use a word or phrase then String.hashCode() is called and it limits your maximum amount of seeds to 2^32 because of it's implementation.

If you enter your own number or let the system determine the seed then your seed limit is 2^64 seeds.

HOWEVER:

If it's a multiplayer world they implement the nextLong() java function and the limitations of that are 2^48 possible seed options.