I've always been afraid of updating Jenkins or the plugins because things always broke. Always.
That being said, I updated a few instances to 2.0, immediately applied all plugin updates and things kept working as before. That was a surprise. I was already prepared to spend hours trying to find why our jobs were failing. That was nice.
We have had problems but mainly with plugins. There's basically no mandatory QA process for plugins, nor is there any facility to make it obvious to an updater that an upstream change affects a downstream plugin and might break it.
In my opinion, Jenkins is a product that you really need to have a test instance for, where you either have copies of your builds or you've set up some 'unit test'-type builds to exercise functionality you depend on.
That being said, I updated a few instances to 2.0, immediately applied all plugin updates and things kept working as before. That was a surprise. I was already prepared to spend hours trying to find why our jobs were failing. That was nice.