I think keeping up with current affairs is important. You need to understand the world in order to participate in it.
Here's some reasons why you should follow current affairs: so you can be a more informed voter; so you can held safeguard the democracy you benefit from; so you can be aware of threats to your livelihood and social environment; so you can make informed decisions about how you live your life (are there particular charitable causes that need my time or money right now?); so you understand the politics of situations when you travel; etc etc.
I think what most people mean when they say they don't like the news is that they can't stand 24 hour news, or find it too depressing, or too much of a distraction. But those things are artefacts of how you consume the news, not the concept of following world events itself.
After following current affairs avidly since being a teenager, I would recommend subscribing to the Economist and also regularly reading a left-leaning outlet (I read the Guardian, it's better than most). I'd also recommend listening to a sophisticated radio station (Radio 4 in the UK; I believe NPR is good for the US, although I'm not an expert), and less frequently watching high-quality news coverage (Ch 4 news or the Andrew Marr show in the UK). Combine that with a general scan of other sites like the BBC, NYT, Al-Jazeera, etc. etc. to ensure you're not missing any major stories. Spend some time understanding the story of the world.
Incidentally, one really nice consequence of staying informed is when you meet people from other countries. Just last night I met a bartender from Columbia and he was impressed with my understanding of the political situation, the FARC guerrillas, the referendum etc. ... it provided a good starting point, and then he gave me a more detailed insider's view.