How to remove a field completely from a MongoDB document?

Try this: If your collection was 'example'

db.example.update({}, {$unset: {words:1}}, false, true);

Refer this:

http://www.mongodb.org/display/DOCS/Updating#Updating-%24unset

UPDATE:

The above link no longer covers '$unset'ing. Be sure to add {multi: true} if you want to remove this field from all of the documents in the collection; otherwise, it will only remove it from the first document it finds that matches. See this for updated documentation:

https://docs.mongodb.com/manual/reference/operator/update/unset/

Example:

db.example.update({}, {$unset: {words:1}} , {multi: true});

In the beginning, I did not get why the question has a bounty (I thought that the question has a nice answer and there is nothing to add), but then I noticed that the answer which was accepted and upvoted 15 times was actually wrong!

Yes, you have to use $unset operator, but this unset is going to remove the words key which does not exist for a document for a collection. So basically it will do nothing.

So you need to tell Mongo to look in the document tags and then in the words using dot notation. So the correct query is.

db.example.update(
  {},
  { $unset: {'tags.words':1}},
  false, true
)

Just for the sake of completion, I will refer to another way of doing it, which is much worse, but this way you can change the field with any custom code (even based on another field from this document).