Mixpanel has a free tier for their engagement and people plans. I'm only played around with Mixpanel a little bit. I'm a little more well versed in KISSmetrics

Mixpanel has a free tier for their engagement and people plans. I'm only played around with Mixpanel a little bit. I'm a little more well versed in KISSmetrics but they don't have a free tier. Mailchimp isn't an analytics tool but they offer analytics on their mail campaigns and they have a fairly large free tier.