However, I disagree with the only two more emails part. Email is a very strong tool, often underestimated.
Depending upon the stage in the lifecycle, you can send emails to: 1) Convert trial signups to Activated users. 2) Re-activating users. 3) Convert activated users to paying customers. 4) Upselling paying customers. 5) Improving retention.
It goes without saying all emails should depend on what the customer has done with your app so far. For example, if I'm losing an activated user, the script can check which important sections of my app have not been visited and send an email informing about what he missed and why it's important - you get the point.
So, it is best to collect extensive data about how your customers use your app and fire customized emails accordingly.
I normally don't send more than 2 emails a week for the first one month and then this number decreases. I'm wondering what others do here.