How to safely upgrade plugins and test?

It seems like every couple days or so, there is an update available for a plugin. I get really nervous upgrading plugins especially since I have 20+ sites using various plugins. Just recently, I upgraded Subscribe2 and turned out there was a major bug that affected multi-sites. It killed a few of my sub-sites and had to revert back.

Is there a recommended way to upgrade plugins carefully? What is a good way to test WordPress’s health after the plugin upgrades to ensure everything is still functioning as before. Updating plugins blindly is not something I want to do anymore. Any help or advice would be greatly appreciated.