Estimation by observing the effects of wind

The Beaufort Scale (history; use at sea)
The Beaufort Scale (sea and land versions)
The Beaufort Scale (for land use; nautical mile converter)
The Fujita Tornado Damage Scale

Instruments

Dixie-cup Anemometer
cup anemometer
propeller-vane anemometer
sonic anemometer
buoy-mounted: diagram, photo
ACARS (Aircraft Communications Addressing and Reporting System): Most ACARS-equipped
aircraft provide latitude, longitude, altitude, time, temperature, wind direction, and wind speed.
scatterometer

Analyses

ADAS Analysis of Surface Wind Speed
  10 km Resolution Western U.S. : Current Image
  Wasatch Front : Current Image

Current Southwest Regional Surface Map

US Wind Streamlines

NWS Surface Analysis Fax Charts (more info)
  North America: sample: tif, png
  Pacific: sample: tif, png
  chart reference guide

TAO/TRITON buoy array (more info)
  Sea surface temperature and winds: current 5-day mean

ACARS (more info)
  Santa Ana winds: sounding, descent track

Measuring Ocean Winds from Space (more info)
 Interpolated animation of global winds as viewed from the SeaWinds scatterometer on August 1, 1999: 3.3 meg QuickTime Movie

Grand Island tornadoes (from T. Theodore Fujita: His Contribution to Tornado Knowledge through Damage Documentation and the Fujita Scale.)