If you mean downwards (to bedrock) 63+ depending how high you are, low biomes like plains fall about this height. This is the same if you are using pocket edition or on an Xbox.
If you mean across land, it depends on the version. If you are on 1.7.(anything) which you probably are it is 30,000,000 blocks from your spawn in any direction until you reach an invisible forcefield. You can teleport to the other side using the /tp command but many glitches occur there. In a recent 1.8 snapshot and since the edge of the world is customisable, look at mojangs instructional video to find out what the command is. I believe the default is still 30,000,000 blocks but you can change it. This is only on PC I am not sure about Xbox, but it is probably the same, or similar.
In Pocket edition the world is very small, only a few hundred wide and long, outside this border you cannot get to and no blocks exist.
Hope you and any other curious fans found this helpful.
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Minecraft characters are approximately 2 blocks high.
309,987,908,986,098,890,120,012,210.
If you're talking about a Minecraft world, there is no limit. The world keeps randomly generating. If you're talking about the map item, it changes. As of 1.4 you can expand a map to make it show more blocks.
4 blocks.
It depends on how many blocks you placed and how far you have traveled.