When I started flying in 1979, ATIS was some kind of magic. You could just dial up the frequency and you got weather. In the Air Force back then, getting weather meant calling the weather shop via UHF or getting a phone patch via HF. Of course we could also call up the nearest Flight Service Station and have the weather described to us. I got my first taste of "on line" weather from XM Satellite. The weather products were limited to the U.S., were delayed by ten or twenty minutes, and the resolution was poor. But it was better than anything else out there.
— James Albright
Over the last ten years I lamented the fact I got better weather on my smart-phone than I did on my smart airplane. But now with high-speed Internet in the cockpit, we got it all. Here are some online sources to choose from.
Note: Some of the website imagery is very large and will take a lot of bandwidth. (You might consider viewing them before the flight instead.) I'll make note of those individually. Don't forget to check your flight planning Apps, such as ForeFlight and ARINCDirect, which can display near real time weather right onto your route of flight. There are also weather Apps available for your iPad.
BBC weather map
The beauty of this product is that it gives you a visual forecast of weather systems in the future.
Geostationary Operational Environmental Satellite (GOES)
The NOAA's GOES satellite senses electromagnetic energy at five wavelengths. Of greatest use to us as pilots are the Infrared and visible imagery.
GOES image viewer
This is an interactive view of the Western Hemisphere with all sorts of imagery available. The Geo-Color Animated Loop or Animated GIF selections provide great detail but are data-intensive (on the order of 12 MB) so you might want to view these before flight.
Japan's Meteorological Satellite Center
The Japanese have their own satellite dedicated to complete views of the Japanese islands.
National and Central Pacific Hurricane Center
The National Hurricane Center and Central Pacific Hurricane Center website is hosted by the National Oceanic and Atmospheric Administration and offers satellite imagery of the Atlantic and Pacific. The loops are especially useful for getting a sense of how the weather is moving.
NESDIS Tropical Cyclone Products
The National Environmental Satellite, Data and Information Service (NESDIS) issues tropical cyclone imagery that can be critical to those flying in the Pacific and Indian Oceans.
NOAA Geostationary Satellite Server
Sometimes you just want the big picture. These geostationary satellites are parked over their parts of the world to provide just that.
U.S. Aviation Weather
For weather over the Continental United States, it is hard to beat this NOAA site. It used to be a one-stop--shop for all things weather in the CONUS. But now you will also need to visit https://radar.weather.gov/ for national Doppler radar information.
U.S. Radar Weather
Imagine being able to stitch together every FAA, NWS, and DoD weather radar site so you had access to it all? Well, here it is.