This is a question I like to ask our more developed portfolio companies who have built large markets/networks/user bases. I ask them "if you were a startup and you wanted to compete with our company, how would you go about it?"
I think it is very important to understand your weakest flanks/vulnerabilities and then shore them up. If someone will compete with you by coming at the market "mobile only" while you struggle with maintaining a large web and mobile presence, then you should know that. And it probably means you need to rethink your mobile strategy so you can close off that open flank. If someone will compete with you by offering a free version of what you charge $10,000 a month for, then maybe you need to think about a freemium offering to close off that open flank.
This question is a particularly good one to ask at a senior management offsite or board offsite/strategy session. It often leads to changes in priorities and/or strategy. I have engaged in many excellent strategic discussions that came out of asking this very simple question.
I thought of this today when reading Benedict Evans' post on how one might do this to LinkedIn. I would suggest the folks at LinkedIn read it as well as anyone else who likes to think this way.