Historical NWS GFS forecast data
It all depends on the region you are interested on. For the North America region, you could use the North American Regional Reanalysis (NARR). 

NARR is a "high resolution combined model and assimilated dataset. It covers 1979 to near present and is provided 8-times daily, daily and monthly". The best and easiest way to access the data is through NOMADS. There you will find data in several different formats (netCDF, GRIB...) and it has a resolution of around 32km.

If your interest is in global data, then you could try the NCEP/NCAR Reanalysis. It is a global reanalysis of the atmosphere from 1948 to the present with a resolution of 2.5 degrees. There is also the NCEP/DOE reanalysis with a similar footprint. I think you can get both of them from NOMADS.

All these products are reanalysis (therefore not forecast) products. If your interest is in forecast products, then you can use the North American Mesoscale (NAM) product. It has a resolution of 12km and it is available through NOMADS. The model they are currently running is a version of the Weather Research &amp; Forecasting - Nonhydrostatic Mesoscale Model (WRF-NMM).

There is a complete list of NOAA model products available and a brief description of each in the NOAA NOMADS page.