If you just apply a flat, continuous texture to a UV mapped model, it will tend to do that. Imagine that the map is an opened out version of the model's surface; somewhere there has to be a seam, and there are usually several. You would normally distort your map to achieve a seam free appearance, but this depends on knowing which bits join to which. SnowSultan has a series of seam guides in freestuff that will help.