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Dart

I guess this would be the classical way of doing recursion without any actual recursive function. No function below refers to itself by name, directly or indirectly.

(Try it at dartpad.dartlang.org)

// Strict fixpoint operator.
fix(f) => ((x)=>f(x(x))) ((x)=>(v)=>f(x(x))(v));
// Repeat action while it returns true.
void repeat(action) { fix((rep1) => (b) { if (b()) rep1(b); })(action); }

main() {
  int x = 0;
  repeat(() {  
    print(++x);
    return x < 10;
  });
}