Turbulence, especially clear air, is often reported as a "ride report". It doesn't come or go quickly, so ATC can often build up a pretty accurate picture of where it is and that will be passed along. The frequency of these reports varies around the world...ranging from very common (in the USA) to utterly non existent. To a degree they aren't necessary, as they are generally predicted on our flight plans and weather forecasts, and other than limited climbs or descents, there's not much you can do to avoid them.
Weather associated with storms, etc, isn't reported at all. It's a pretty basic assumption that you have radar and know how to use it. Generally you find a track through the weather that will work for you (normally just an offset to either side), and get ATC to approve that. In the USA, because it's a bit too busy to have aircraft sorting out their own act, ATC tend to reroute flights (via airways) to track well clear of offending storms.
Overall there is very little chatter between aircraft.