Hands-down, news.google.com. I've been using it for a few months now, and it fits the bill in many respects. I like it for several reasons.
1. It's broad, but narrow. It's like scanning major news publications for the latest news on certain topics. It isn't necessarily the most timely--breaking news is better at one of the major news agency, but hunting down 3-5 stories on an item that happened a day or two ago is no sweat.
2. Keeps me up to date with the latest news on certain topics. Just like doing a Google search of the Web, the search engine brings back results. You can sort them by date or relevance--I use both at times. I have certain topics I search regularly (such as variations on "bible translation"), and I can see the latest news.
3. Great for news on othewise hard-to-find topics. We had a missionary over in the Ivory Coast, and trying to find news on what was happening was difficult, until I tried the Google search. It was great for keeping up to date with those events. Other current events I've used it on include the elections in Ukraine and more recently the tsunamis.
So there are a lot of things to like about it. Things I'm not as wild about:
1. Repetition. This is the biggest downside. You don't realize how broadly a news service like AP is distributed until you see how many different times the same headline pops up. On the regular Google search, they eliminate duplicates. This is a definite shortcoming.
2. Search Limits. This is the flip-side of the positive listed above. The same limitations of scope that prevent searches from becoming overwhelming also prevent them from reaching too far back. I suppose the most apropos analogy would be stacking up daily papers in your house to keep track of what was going on--it wouldn't take too long before they would get out of control. But at times this can be frustrating, when you are dealing with developing stories.
3. Inclusion of subscription/registration websites. This is more of a minor irritation, but it seems like many of the stories I'm interested in require a registration at the website. I could probably do it, but who has the time?
Overall, the positives outweigh the negatives (at least on a qualitative basis), so Google is my number one choice for news. (Did I mention they have multiple languages and countries?)