Nodes with no tags.

Nodes with no tags can serve the following purposes:

• they could form an "ellipsis" (three of them in a row) denoting that a way needs continuation.
• they could be from an ongoing or botched import, where nodes were imported first and some ways using these nodes will be imported later, or were planned to be imported later.
• they could be a work-in-progress of someone who - for whatever reason - decided to draw nodes first and tag or use them later.
• they could be part of a way or a relation; depending on what editor and edit mode you are using, it may not be immediately obvious whether a node is part of a relation.

If the un-tagged nodes are on their own, not part of any way or relation, and older than a few months I'd reckon it is safe to delete them, although out of courtesy to your fellow mappers you could find out who created them and send them a message before you do.