The best weather forecast model in the world is run by ECMWF (European Center for Medium-range Weather Forecasting http://ecmwf.int/)

They have a good web page to find out about their performance with comparisons to other centers. Check out the ECMWF page Quality of our forecasts for more in depth answers, I’ll just point out a quick simple response.

Below is maybe the most key variable for weather forecasting, 500 hPa geopotential height. It shows how correct the air state has been forecast in the free atmosphere (~5 km height). The different colors are for how long the forecast was and the percentage shows if the forecast was within a certain threshold correct. The biggest jump in quality was around 2000 then satellite observations made northern and southern hemisphere forecast much more equal, but also since then quality has improved. 7 day forecasts have in the last 10 years been in more than 70% of cases been correct. That is significant then 7 day forecast pre 2000 were mostly useless.