I think it's important to an extent.
I don't think a writer needs to delve into current events that deeply - unless of course they're writing timely material like a thriller or something along those lines where a good working knowledge of current events would probably be necessary.
But, even if writing fantasy or a memoir or historical fiction, I still think it's a good idea for a writer to at least be aware of what's going on in the world today.
One of the key elements to being a good writer and writing a compelling story, I feel, is an understanding of human nature.
In order to do this you must observe the world around you and it's participants, which would naturally include current events.
Also, I think a good knowledge of current events and the world around you helps you make your work more accessible to larger volumes of people by allowing you to be able to find more points of connection, so to speak, with your reader.
It's all about getting your reader to identify and become involved in your story and I think knowing and being aware of certain parallel events in the real world today can help you to find the words to get your reader to see and feel the similar events in your fictional world.