Before I take several people on a short trip in my car, should I have them sign a release?

You cannot sign away a person's right to sue on personal injury in the situation you are describing per se.  Further, if you are going on a short trip, is it still out of state or are you planning on staying in the state.  This is an important factor because it can determine where the lawsuit would be filed, which laws would be used should you get into an accident. 

As a driver, you are required to use ordinary care if you are driving others who are your guests and non-paying.  There is a higher burden if you are hired (like a motor carrier, bus driver, limo driver, etc.).  Generally, the requirement to use ordinary or reasonable care exists whether or not your state has a guest statute.  If a guest statute exists, or one exists in the state in which the accident occurs, it may limit the liability of the driver and will require liability under circumstances wherein the driver was grossly negligent or used willful or wanton disregard for safety (so his or her actions have to be really serious). 

Further, the guests have to use reasonable care and this could also limit their recovery amount if they were negligent or caused the driver to be distracted while driving.