Another simple and often overlooked cause to the issue you're seeing is that the person or persons who made the texture map did not extend the texture 2 to 4 pixels beyond the border of the UV template. It's a classic mistake.  A simple way to resolve this, would be to load the texture into a image editor, choose a dominant color from the texture, and fill the empty space around the texture with that color. That should make the seam less noticeable.