[richdougherty]

One way to look at it is they let you do "low level functional programming", where you can write code that jumps around without using stack space.

If you think about all the standard statements in a language - if, while, async, etc - all of these kinds of constructs can be built out of normal functions once you have tail calls. This makes the language more extensible and reduces the need to introduce new kinds of built-in language constructs and allows more experimentation.

They're really useful for input processing/parsing, recursion, implementing algorithms, etc.

Another way to think about it is that functions can become little 'named blocks' with defined inputs and outputs, and you can combine them together without worrying so much about the runtime costs of functions that take up stack space. So if you have a function with lots of if conditions, while loops, etc, you can convert it into these 'named blocks' instead, which makes maintenance easier.

There are lots of examples. In a way, the fact that none of the main imperative languages support this simple runtime feature is what's stopping people from realising how great tail calls are. There's a bit of a Catch-22 happening.