Brett,

It depends on the model...

Most models are run based on 00z and 12z data...primarily radiosondes (weather balloons) lanuched at that time. In more recent years, more data such as aircraft reports, surface data, satellite winds, etc, are being incorporated into the model inital analysis. Here is a general guide to run times of various models.

ETA 00z and 12z to 84 hrs, 06 and 18z to 60 hrs.
AVN/GFS 00z to 384 hrs, 12z to 240 hrs, 06 and 18z to 72 hrs
NGM 00z and 12z to 48 hrs
UKMET 00z and 12z to 144 hrs
ECMWF 00z and 12z to 240 hrs
Canadian GEM 00z and 12z to 144 hrs
NOGAPS 00z and 12z to 144 hrs

Then the track models...
GFDL, GFDN upon request, usually at 00, 06, 12, 18Z to 144 hrs
LBAR, BAM's, A98E, SHIPS, ESHIPS, DSHIPS 00z and 12z to 72 hrs.

the RUC is run every hour (hi-res version RUC2) to 12 hrs, or every 3 hrs to 24 hrs.

Every time a model is run, the inital data is changed...so each run is discreet and different.