Such expressions as
are plural or singular?
E.g. I like to watch drama/TV series or I like to watch a drama/TV series?
"Series" can be singular or plural depending on context. Both of your sentences are therefore correct but different.
uses series as a plural and means you like to watch a number of different TV shows.
uses series as singular and means you like to watch one TV show.
The word series is both singular and plural.
Good information from thefreedictionary quoting American Heritage Dictionary as its source:
Our concern is series in broadcasting. So,
Having this said, you watch a TV series. And yes, do consider Nigel's answer if you are specific about one particular program or series.