This is a classic problem with UV atlases and filtering in renderers.

In Blender Internal you can avoid the white lines by disabling mip maps and setting the filter size low enough. You then get aliasing instead though, and can't get rid of it because Blender Internal will only sample the texture once per pixel.

In Cycles such aliasing is solved by using more AA samples which will sample the texture multiple times per pixel, but that's slower to render. As far as I know that's the only solution to both avoid the bleeding and aliasing problems, so Blender Internal would need to get some way to sample textures multiple times per pixel to solve this.

I found a temporary fix for this on BI.
Turn ON transparency on Material & Alpha influence on texture.
(something to investigate there)

But still, it looks pretty bad on viewport & BGE.
Since we are going to have better GLSL renderer, I think we should look into solving this properly.

I don't think enabling alpha really solves the problem. In the attached .blend file the space between the UV islands has alpha 0, and enabling alpha makes it black, which in this test file happens to be the same color as the UV islands themselves. But if the islands have a different color the issue shows up again.

If you want to solve this fully for GLSL, I guess you should look into limiting the mipmap levels to a certain number (e.g. 3 for pixel bleed 8). Then you get some aliasing which you can solve with multisample if necessary. Although I would expect the solution typically used in games to be just bleeding more than 8 pixels.

More renders of the case.

@Sergey Sharybin (sergey)

"surely we can improve BI to support maximum mipmap level or to do more AA samples"

How that works? I'm curious.