Question: I have a single select drop down and need to enable the user to clear his selection too.

Is it elegant to do this:

[![enter image description here](https://i.stack.imgur.com/UgB2z.png)](https://i.stack.imgur.com/UgB2z.png)

Or, on selection of an option should the drop down be hidden, showing the selected items text along with the `X` mark beside it clicking on which the drop down would be shown again?

Answer: 
The phrase 'Please select a thing' implies that the user has not selected anything from the dropdown yet. To clear a selection, you can have two alternatives:

1. Add a 'Clear selection' choice in the dropdown.
2. Allow the user to switch back to 'Please select a thing' which will imply that the selection previously made has been undone.

The [x] next to your dropdown confuses me. It seems like it would remove the entire dropdown, instead of just clearing the selection. My suggestion would be to use the dropdown itself for clearing options, staying within recognised UI patterns.
Your proposal looks fine to me as it is. 

I would say that you should not mess about with the interface. Do not have it morphing unless it is absolutely warranted... because that makes for a confusing user experience.

Also in this particular case: no, do not force the user to click the [x] in order to make a new selection. It will be particularly annoying in case of mis-clicks.