Heroku Revamps with Logs, Processes and Node.js
gigaom.com
gigaom.com
If you want to do logging out of your app for free and have up to a week's retention, you could use Logglier: https://github.com/freeformz/logglier and a free Loggly account: http://logg.ly/signup. You won't get the Heroku bits of the stack, like cache hits and such, but you can at least see what the app is doing.
You can get a free log aggregation account at https://papertrailapp.com/ and it'll give you a target URL to configure (and irl karma for supporting a bootstrapped startup).
The logs won't contain non-Rails requests (Varnish/cache, API deploys) but they're much better than nothing.