Recs.
Updated
Mixpanel is a very popular, event-driven analytics tool. It supports all the features a SaaS web-app would expect as well as some killer additions such as "engage" that lets you use your analytics to send highly targeted emails to your users and the ability to see completely live data.
Specs
Pros
Pro Improve retention with "Engage"
Mixpanel allows you analyse the conditions where your users churn from your application and then send targeted emails designed to bring them back. This is an amazingly powerful feature that really bridges the gap between analyzing the data and acting on it.
Pro Contact users directly through the people page
Mixpanel allows you to directly contact users from the people dashboard via push notifications, sms, and email. After viewing the user history, or filtering on events and metrics, you can send an individual user, or a segment direct messages.