javascript: recursive anonymous function?

You can give the function a name, even when you're creating the function as a value and not a "function declaration" statement. In other words:

(function foo() { foo(); })();

is a stack-blowing recursive function. Now, that said, you probably don't may not want to do this in general because there are some weird problems with various implementations of Javascript. (note — that's a fairly old comment; some/many/all of the problems described in Kangax's blog post may be fixed in more modern browsers.)

When you give a name like that, the name is not visible outside the function (well, it's not supposed to be; that's one of the weirdnesses). It's like "letrec" in Lisp.

As for arguments.callee, that's disallowed in "strict" mode and generally is considered a bad thing, because it makes some optimizations hard. It's also much slower than one might expect.

edit — If you want to have the effect of an "anonymous" function that can call itself, you can do something like this (assuming you're passing the function as a callback or something like that):

asyncThingWithCallback(params, (function() {
  function recursive() {
    if (timeToStop())
      return whatever();
    recursive(moreWork);
  }
  return recursive;
})());

What that does is define a function with a nice, safe, not-broken-in-IE function declaration statement, creating a local function whose name will not pollute the global namespace. The wrapper (truly anonymous) function just returns that local function.

People talked about the Y combinator in comments, but no one wrote it as an answer.

The Y combinator can be defined in javascript as follows: (thanks to steamer25 for the link)

var Y = function (gen) {
  return (function(f) {
    return f(f);
  }(function(f) {
    return gen(function() {
      return f(f).apply(null, arguments);
    });
  }));
}

And when you want to pass your anonymous function:

(Y(function(recur) {
  return function(data) {
    data = data+1;
    var nothing = function() {
      recur(data);
    }
    nothing();
  }
})());

The most important thing to note about this solution is that you shouldn't use it.