ECMWF (European Centre for Medium-Range Weather Forecasts) is sometimes informally known in the USA as the "European model". More info available at
www.ecmwf.com
Resolution is 0.1° in lat/lon (~9km).
The forecast output is produced every three hours for first 144 hours, six hourly through day 10.
GFS (Global Forecast System) - the model is operated by the United States' National Weather Service (NWS)
Resolution is ~13 km.
The forecast output is produced every hour for the first 120 hours, three hourly through day 10.
Local models:
NEMS - This model is produced by Meteoblue.com, Swiss weather geniuses
Resolution is ~4 km, available only for Europe.