This is one of the easiest, most obvious things to do. One of the key reasons to follow other people is to listen to what they have to say. Their tweets may be informative, clever, funny, interesting or useful.
Even outside breaking news, people find other people's content just as informative ... and there's an awful lot of content out there to sift through. Provide a valuable service to the Twitter community in your field or specialty area by acting as a filter or curator: Find topical articles, blog posts, stats and facts, aggregated news pages or other sources of similar information–the same content you might already be tracking for professional reasons–and then tweet out those links.
Don't be afraid to tweet great content more than once. People forget that with such a large Twitterverse and only so many hours in a day, some of your best content might go unseen.
Similarly, good content has staying power and its relevancy a few months or even years ago might be good to revisit today. Feel free to tweet content multiple times or tweet from the archives. Just spread it out over time, acknowledge that re-post (see example below), and mix it up.