There isn't an out of the box feature you can enable however take a look at the following post which provides a similar functionality on a process by process basis.  Note that there is a limitation in K2 that I've experienced where errors on destination user's will not always be caught by K2's exception handling.

http://www.k2underground.com/forums/t/11716.aspx

Another potential tool to use if provided on the blackmarket.  I haven't actually used this tool but the advantage is once enabled it should work for every process.

http://www.k2underground.com/groups/k2_process_error_notification_service_k2_pens/default.aspx

Thanks for the response.

An alternative solution may be to create a trigger on the K2Server._ErrorLog SQL table.
Would this be ok, or should I steer clear of doing anything like this?

All I need to know is that a process instance has gone into error so that I can then go and investigate.

Conceptually it would probably work but I'm sure it would be unsupported and not recommended by K2 as it may cause unexpected behaviour.  Also it might be overwritten by new updates that you apply to K2.

I cannot get the Email Notifications to work.  I can send a test email, but process errors are not reported.  I checked the server settings directly from the strings library and all settings seem to be correct.  Any help or insight is greatly appreciated.