Photoshop has a handy feature that allows you to save images for web use. It allows you to save images as JPGs, GIFs, and PNGs. It also allows you to resize your image before saving it. Some time ago I noticed that some of my images had a thin white border around them. I believe this to be a result of image resizing. After some trial and error, I found a couple of ways to fix this problem.
Before you "Save For Web"
1. Try to resize your image first: Image -> Image Size...
2. Try to "Flatten" your layers first: Layer -> Flatten Image
If all else fails open your file, after you've Saved For Web, and paint around the edges with the same color as your background. Once you're done painting just: File -> Save