AccuWeather.com? This is from their "About" page:
AccuWeather, established in 1962, is the World's Weather Authority. We provide local forecasts for everywhere in the United States and over two million locations worldwide. We also provide our products and services to more than 175,000 paying customers in media, business, government and institutions. Our headquarters in State College, PA, is home to the greatest number of forecast meteorologists in one location anywhere in the world.
AccuWeather.com recently changed their website, so if you haven't seen it in a while, you might want to stop by and see if you like it. Searching is easy: just type in your location and click "Go." If you need a location outside the US, use the "World," "Canada," or "UK/Ireland" links at the top left.
The homepage has maps and articles - scroll down to see them. You can also mouse over the menus for more options under "Forecast," "Radar & Maps," "News & Video," and more.
Click the "Downloads" link at the bottom of the screen for widgets and phone apps. You can also follow them on Facebook and Twitter.
National Weather Service (also www.weather.gov). This website is the only one of the four mentioned here that does not have ads and that only has US weather. The graphics are not as slick, but they have the familiar look of many TV stations. See the links on the left for warnings and forecasts. To keep you informed on the go, they offer RSS feeds for warnings and forecasts, and you can sign up for text messages.
weather.com (not to be confused with the NWS site, weather.gov). It looks slightly redesigned since the last time I used it, so give it a try if you haven't seen it recently. (It used to be video-intensive, which slowed loading time.) Although this cable TV station is shown in the US, the website offers world locations. The menu across the top offers "News," "Travel," "Driving Conditions," and more. There are some news items and articles on the homepage.
Forecasts are given in various spans of time, from hour-by-hour to 10-day. You can also see yesterday's weather information plus averages and historical information.
Scroll down to the bottom of the screen for widgets and browser extensions. You can also get text alerts and RSS feeds.
Weather Underground says it was "the first Internet weather service" (see their About Us page for a history). There is no separate link for international weather - just type your location into the search box. This one tends to be my default because the 5-day forecast in the form of graphics and a short blurb is right on the results page. You can click for more information, but I like the quick show of information. I also like having the ability to see the moon phases and a star chart if I want. They also provide historical weather info and averages.
There are not as many articles here as on AccuWeather, but there are a few. You can upload your own photos and videos to share, and you can follow them on Facebook and Twitter. They also have RSS feeds as well as widgets and phone apps (click "Download" in the upper right).
I've mentioned Twitter in a couple of write-ups, but there's one more site I want to mention: Severe Weather Alert System (SWAS). (Thanks to TechCrunch for the blog post.) Follow the steps outlined on the homepage to sign up for local weather alerts, delivered to your Twitter account.