A language is a tool, not the end in itself. We need to be, or strive to be, masters of computer programming, not of computer languages.
Of course, a master knows its tools. He has many tools in his toolset and chooses the ones that better fit the task he is working at. Sometimes he may need to use a new tool, which he learns and adds to the toolset.
New languages rarely introduce substantially new concepts, mostly new ways to represent those concepts and put them together in a better way. However, if we are talking about new concepts, not just new languages, that is different. Other commenters have mentioned functional versus imperative programming style (enforced, or at least suggested, by the language) and so on. Learning new concepts makes us better programmers in older languages too.
Of course, a master knows its tools. He has many tools in his toolset and chooses the ones that better fit the task he is working at. Sometimes he may need to use a new tool, which he learns and adds to the toolset.
New languages rarely introduce substantially new concepts, mostly new ways to represent those concepts and put them together in a better way. However, if we are talking about new concepts, not just new languages, that is different. Other commenters have mentioned functional versus imperative programming style (enforced, or at least suggested, by the language) and so on. Learning new concepts makes us better programmers in older languages too.