The Legendary Rule always applies. Some play groups have a "house rule" that it doesn't apply to opposing players' Commanders, but that isn't part of the standard rules for the format.
Commander (EDH) is subject to the Legend rule; they will be put into the graveyard or command zone at the same time as any other Legendary creatures with the same name.
Most people have a house rule that says if two people have the same Commander then the legend rule doesn't apply between those two CARDS. If someone gets another of that legend into play somehow they all die to the legend rule.
This is why Animar, Intet, and Edric, Spymaster of Trest are the only legends I run in deck:the-splintered-mirror. Riku just doesn't work well with legends.
at our magic we all choose a commander so there are no conflicts, then where u finished in the last league is what number u get to pick ur commander
so if u won the league u get to choose ur commander first, second chooses second etc. never a clash.
Polaris was right in saying "If someone gets another of that legend into play somehow they all die to the legend rule."
I've heard a house rule that some people play by where if there are two of the same legendary on the field, and one of them is a general, then the general stays and the nongeneral goes to the graveyard.
I think it's basically a rule to prevent clone effects from killing generals. It's definitely a rule that someone running a general like Thrun or Uril would appreciate.