Wine is still under development, so it cannot yet offer the same stability and ease of use as Windows. However, it is improving rapidly and has recently reached the stage where you can run WinBUGS on it without too much inconvenience. I can't recommend using Wine for serious statistical analysis because it is still alpha software. However, you may find it useful for teaching or demonstration purposes in an environment where there Windows is unavailable. This was the reason I started looking into WinBUGS on Wine.
Wine is free software and comes with no warranty.
Use it at your own risk. Installation guide . Known problems . A list of problems you may encounter working with WinBUGS on wine.