Is it possible to redirect console output to a log file in IntelliJ like Eclipse?

In more recent versions of IntelliJ this is possible. Go to the "Logs" tab of a run configuration. There is a "Save console output to file option".

I'm on IntelliJ 13.1.3 but I think this feature has been around for a while.

UPDATE: this feature is available in IDEA 11.

Not possible in IDEA at the moment, I've submitted a new feature request. Feel free to vote.

A workaround could be implemented using wrapper class with main() method which will redirect stdout and stderr to files and then run the main class of your application.