I'll read the times sometimes, love the new smaller "tabloid" size. If I buy a normal tabloid rag then I've read it in about 15 minutes and I'm none the wizer about the world. What I love to do these days is go on a wiki crawl where you start off on one topic(wikipedia) and just click on links and end up learning about totally weird things, it really is good fun even though a lot of the "facts" are a bit dubious.
For daily news and sport I'll normally read bbc.co.uk/news