Updated Oct 2018
If you are watching or recording a live broadcast, by aerial, satellite or streaming online (iplayer,Netflix, Prime etc ) …… YES you should have a license.
If you are playing content that you downloaded as a file, rather than streamed, then No, you don’t need one, as it isn’t a ‘live’ broadcast. Note this doesn’t apply to downloading BBC programmes on iplayer – you Do need a license it that case.
Other European countries have reciprocal arrangements.
This is a common query by landlords with tenants from abroad, so if you’re renting accommodation, do look into this!
If you are a lodger or the room is not self contained, or you don’t have your own separate tenancy agreement, then you probably don’t need a license, you would be covered by the home owners license, but do check with tvlicensing to be sure .
More Information can be found on the BBC site, tvlicensing.co.uk
This is the interpretation of the legal situation re tv licensing, of the author and should not be relied on as a defence ! Please read the official website above.