On Venus, there is really inhospitable weather, as well as within the gas giants in our solar system. Are there examples of even more extreme weather on planets found in other solar systems than ours?
I'd say that HD 189733b is a good candidate for the most extreme known weather on another planet (outside our Solar System).
According to some recent news accounts, the atmospheric temperature is believed to be over 1000° C, with 7000 kph winds. (For comparison to the data in Rory Alsop's answer, that's about 1900 meters per second.)
And it rains molten glass. Sideways.
UPDATE : As Guillochon points out in a comment, HD 80606 b likely has even higher winds, though they're not continuous. It's a Jovian with an extremely eccentric orbit. Quoting the Wikipedia article:
which, in civilized units, is about 4800 meters/second. Probably no molten glass rain, though, so it's not clear that it's more "extreme".
So far, we don't have anywhere near enough detail to identify weather on planets in other star systems. We even have difficulty working out the size of some of them, so it may be a while till we can get a good idea as to weather.
So the answer is going to be in our solar system.
As for extremes, we have a couple of options:
Saturn and Neptune have the highest wind speeds, and as Neptune has the most extreme difference between East-West and West-East winds, I would be tempted to say it has the most extreme weather.
Pluto is incredibly cold, but it doesn't vary much, so should we call it an extreme? Mercury has a much more extreme range of temperatures. From sunside (over 400C) to coldside (almost -200C) gives a difference of 600 degrees Celsius!