If you're looking for Google Analytics-style "high level website stuff" (visitors, pageviews, per-page, yadda yadda): http://haveamint.com/

If you're looking for MixPanel/KissMetrics style arbitrary event tracking, I do not have a good recommendation for you for an OSS or off-the-shelf solution. I'd be interest in hearing others' experiences.

A lot of consulting clients end up rolling their own. You can get pretty far with Postgres or Redis and hourly/daily cron jobs which dump their output to a few admin screens. They're several orders of magnitude more expensive than the SaaS alternatives (+), marketing can't use them w/o engineering helping out to set them up, and they're generally going to produce less pretty output, but they're often perfectly adequate for decisionmaking.

(+ I struggle to think of a consulting client which does metrics in-house that does not have six figures or more of implicit engineering cost in their metrics systems.)

I've read a previous thread a few months ago asking for advices on analytics for a startup, you can find it here : http://news.ycombinator.com/item?id=4707903

In it you can find multiple open source solutions such as Piwik (see sheff comment), snowplow (https://github.com/snowplow/snowplow) and Graphite (http://graphite.wikidot.com/start).

Hope this helps.

Didn't know about those, thanks. Going to look over them.

We don't need to know where our users come etc, but more following certain events and patterns and how they engage with the app.

Have you looked at Piwik ?

Its open source, fairly well established and can be self hosted.

A list of its main features can be seen here : http://piwik.org/features/list/ .