The safest thing to do is wait until you hear industry leaders talking positively about a particular project, and recommending it for enterprise use. Scan the trade publications for reviews, case studies, and opinion articles that will make you confident that it's getting a wide thumbs-up. Do some searching in trusted publications on the type of application you're looking for, then see what comes up.
For less common types of applications, such as those specific to smaller industries, do some research on your own. You will need to cast a wider net, but you will also have to be more selective. Don't be afraid to contact the core developers of a project that looks promising. Ask about the history of the project - when was it started, what were the original goals, were commerical entities involved? Ask about current development - how many core developers are there, what is the release schedule, what are development plans for the next year? Ask if they can talk about the software in production use.
Ultimately, you have to decide if you are comfortable enough with the project to recommend it for enterprise use. I've done this in my book, The Practical Manager's Guide to Open Source for listings of production-ready open source software for servers, desktops, and custom application development.
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