This topic comes up regularly and always gets people going. In my company (737NG) we encourage pilots to have progress page 2 open, with the tailwind component visible. I believe this is good airmanship.
As has been pointed out in previous threads there appears occasionally to be some dubious reporting of winds at certain southern european airfields. Then again there is no doubt that the tower reported wind takes priority for legal purposes. As with everything it is a question of common sense.
If the tower is reporting a wind within limits and you are landing on a dry 3000 metre runway, then it shouldn't be necessary to go around if the FMS is showing 11 knots tailwind.
On the other hand if you are landing in a heavy rain shower at a small airport in central France it may make sense to err on the side of caution, as recent history has shown.
The FMS wind is but part of the whole picture. Its limitations need to be understood. But if the runway is short and wet and the FMS is telling you something different from the tower then you should be on your guard. Better one go-around too many than one too few!