I'm a big fan of the Guardian, but I'd also suggest that for anyone who has trouble keeping up-to-date, you're probably best off trying out difference sources and finding the one that suits you. Whether that's a source that's extremely left- or right-wing, or somewhere in the middle, if it works for you, chances are you'll read it more. Of course, the next improvement up from this is to read multiple sources to get the fuller, more objective picture.

Also, I've found comedic sources can be great. My two are Have I Got News For You (Friday night comedy panel show based around current afairs - doesn't run all year round though) and Private Eye (satirical current afairs weekly magazine - coincidentally edited by one of the permanent team captains on HIGNFY, Ian Hislop). They can be great fun if you know what they are going to cover already, and they can be a great way for people who are less interested, or just less up-to-date, to get a snapshot of news without having to try too hard to get into it.