You can reorder a Tile by swiping it up and then dragging it to a new position.
If you are using the mouse, you can just drag it to a new position.
As of Q2 2013 a new property of RadTileList is introduced - TileReorderMode. It defines what kind of tile reordering the user may perform and has three options:
None - Tile reordering is disabled.
InGroup - Tile may be placed only inside the original group.
BetweenGroups - Tile may be placed in any group.