Kissmetrics doesn't offer a free tier (they have a 14 day free trial but after that all customers have to commit to an annual contract). Mixpanel does have a free tier.
Full disclosure – I'm a founder at Heap, which is a competitor to both of these products. We do offer a free tier as well.
GoSquared offers event tracking and has a ridiculously simple API to integrate with. No free plans but I think they still have a 14 day trial. Mixpanel is awesome for any kind of phone apps (in addition to regular web funnels).