For years, the generally held answer to this question was 7 but times have changed the sales process beyond recognition. Potential buyers don't have the need to engage with a sales person until much later in the process as they can now just look on the Internet.
The way sales people need to operate hasn't necessarily changed as much though. Sure, they can push potential customers to a website rather than sending a leaflet or brochure but essentially their role is still finding contacts, turning those contacts into prospects and then converting those prospects into sales. In fact it is now too easy to just rely on the Internet.
Another famous cliche is 'people buy from people' but that is as true now as it has ever been. If you're going to be a sales person, be a good one. Sending emails to prospects is simply a cop out. Sure, you might get the occasional reply but most of your messages will be deleted or just slide into the abyss that is at the bottom of everyone's inbox. No, pick up the phone. Ask for the sale (another cliche) arrange to meet. You'll find yourself out of the office far more often, enjoying your job more and getting more sales.
Finally, back to the question about how many touches. The answer is and always has been, it varies. However, whether it's 7 or 107, too many people are guilty of giving up before they hear the word no. If you are repeatedly hearing 'call me back' or can't get through to your prospect, treat that as a 'not yet' and persevere.
Simply put, good sales people aren't afraid of rejection.