I'm currently developing my first bigger game in LibGDX using Maps made with Tiled and Box2D for physics.
It went pretty good so far, but I stumbled across a strange problem: There was some nasty tile bleeding in some areas of my game.
The first solution I found was to round the camera coordinates wich seemed to fix my problem at first, but then it happened again.
Then I found the real solution for this problem:
What you need to do is to add a so called gutter to your spritesheet. A gutter is padding between the single tiles but instead of just beeing transparent pixels the padding will be filled with the edge pixels of each tile.
You can do this with a nice little GIMP python script:
Once you have installed that script, load up your sheet file with GIMP and select "Add Gutter" from the Sprite Sheet submenu in the Filter menu.
You will see a window like this one:
Use a padding of 1, make sure to put the right tile size and enable the Generate Gutter option. When you hit OK it will do its magic and you have your sheet with padding in no time.
The next step is to add the Tileset to Tiled. Select Map>New Tileset. You will see a window like this:
If your map has a transparency color be sure to set that to.
Now you are finished: You have your nice sheet in the Tiled editor and will not experience any tile bleeding while playing your game!
Have fun with this little hint!