Yes, enumerate is useful for that. But even if you did not now about it you could have used count from itertools to get the same effect:

  import itertools
  for (index, item) in zip(itertools.count(0), "hallo"):
      print index, item

Itertools is worth checking out for other goodies, too.

Before enumerate, the standard idiom for this was:

    for i in range(len(a)):
        print i, a[i]

Seriously? You must enjoy your O(n^2).

The sets I'm working on tend not to tend toward infinity.

Yes. But the approach with index only works for actual sets. And if you have actual sets, you might as well use Python's built-in sets.