Satellite is one of the the primary distribution method for NOAA/NWS weather data, called NOAAPORT. Most of the data is available online, though some of it only through paid services. There are a few companies who's primary business is just running a NOAAPORT downlink and packaging up some of the data for reliable internet access by paid clients, as the public NOAA ftp services have limited datasets and tend to get bogged down under heavy load during major severe weather events.
For example, the processing systems for NEXRAD radar spit out data in two formats - Level 2 data is a large lump data file containing an entire volume scan at full resolution, while Level 3 data is further processed and split up into individual radar products at lower resolution and produces many small files. Level 2 is not available over the internet from NOAA, though the University of Iowa has a public level 2 server and there are several paid services that offer level 2 data feeds. Level 3 data is available direct from NOAA FTP, but this is not always reliable. Both are distributed via NOAAPORT, along with much more.
http://www.nws.noaa.gov/om/marine/noaaport.htmThere are also data feeds directly from the GOES satellites, such as the EMWIN feed from GOES-East. EMWIN is also available online, though.