There are no mainstream multi-purpose non Turing complete languages today. There are, however, several non Turing complete domain specific languages. ANSI SQL, regular expressions, data languages (HTML, CSS, JSON, etc), and s-expressions are some notable examples.
There isn't really a benefit for multi-purpose non Turing complete languages. The "much more analyzable" aspect, which I'm assuming is a nod to Rice's theorem, does apply but it doesn't make much sense for languages that target several different application domains, other requirements take precedence. The flexibility of Turing completeness is a lot more important than its complexity. Programming languages, as every other piece of software, are all about trade offs.
For domain specific languages, on the other hand, it might just be the other way around. If you aren't building "one language to rule them all", you are free to implement only the features that make sense for the very specific purpose of your language. And more often than not, Turing completeness is not one of them.