Get names of all keys in the collection

With Kristina's answer as inspiration, I created an open source tool called Variety which does exactly this: https://github.com/variety/variety

You could do this with MapReduce:

mr = db.runCommand({
  "mapreduce" : "my_collection",
  "map" : function() {
    for (var key in this) { emit(key, null); }
  },
  "reduce" : function(key, stuff) { return null; }, 
  "out": "my_collection" + "_keys"
})

Then run distinct on the resulting collection so as to find all the keys:

db[mr.result].distinct("_id")
["foo", "bar", "baz", "_id", ...]