The first side effect of the Far Lands, where the map takes longer to update according to the player's location.
The Far Lands is the area that extends towards what some call the "edges" of the map. It is basically an area that lies as far as 25% from where you are to where the sun is currently. When a player makes it to the far lands, they will witness an excessive amount of lag and the map will be severely distorted. According to Notch, this distortion can be fixed, but since no one is likely to make it to the Far Lands without some form of cheating, he says that he will likely not fix it since he likes the idea of a mysterious world beyond a certain distance.[1]
Getting to the Far Lands
Legitimately getting to the far lands would be an epic task, and probably not that much fun. Instead a level.dat editor could be used to set the player position to the far lands.
The hard limit where chunks get overwritten is at X/Z of 34359738368 (negative or positive). At X/Z of 2147483648, item positions, pathfinding and other things using integers will start to overflow and act weird, usually resulting in minecraft crashing. Before those two points however, things still get weird, such as the map generation, block physics, or the map updating according to where the player is. Using third party programs to get players into the deep far lands will usually result in Minecraft crashing.
Going into the Far Lands can be very dangerous, and can easily result in death or crashing.