There can be several reasons why a workflow that has successfully triggered, hangs for 'no apparent reason'. The first thing I would check is the particular task that it is hanging on. Is that task a background task (ie. requires no user intervention) or is the task a dialog method (ie. a display or approve transaction). If the task is the former then ensure that the task has been checked as BACKGROUND PROCESSING.
If the task requires user intervention yet it does not appear in the appropriate agents inbox then check the workflow log (you can get there via transaction SWI2_FREQ) to see the current agent assignment. If there are no agents assigned then the workflow will just wait for a user that will never come.... Check your agent resolution and consider setting it to 'ERROR' when no agents are determined.
This was first published in July 2001