If I no longer work for my employer, can I take out my retirement fund without penalty?

It depends. There is no exception for the penalty for leaving a job.  

 

You typically need to be 59.5 to take out retirement funds without penalty.  Or, under the "Rule of 55", which is an exception to the early retirement withdrawal penalty, if you are 55 or older, and are withdrawing from your current retirement plan.

 

Some other exceptions include, but are not limited to, disability, medical expenses, education expenses, and emergencies (but emergencies are limited to $1,000).

 

Here is some more information and details on exceptions: An Early Withdrawal From Your 401(k): Understanding the Consequences

If you were age 55 or older when you separated from your employer any distribution from the retirement fund (401(k)), would be free of the 10% early distribution penalty.