Update (thanks to dawmail333):
heroku logs -n 1500
or, to tail the logs live
heroku logs -t
Heroku log documentation
If you need more than a few thousand lines you can Use heroku's Syslog Drains
Alternatively (old method):
$ heroku run rails c
File.open('log/production.log', 'r').each_line { |line| puts line }
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