Q:

Does a 709 ride mean the end of my career?

If I'm required to do a 709 ride following an incident where the plane went off the end of the runway but it wasn't damaged and no one was hurt, what effect does it have on my future as a pilot?
I'm looking to go into commercial aviation (I'm currently a CFI working on hours) and am specifically wondering about how having it in my record will affect interviewing for regionals.

A:

Depends on the reasons the FAA had to justify the need for a 709 ride.  If it was some kind of bureaucratic maneuver without justification for doing so and you pass the ride with flying colors, probably nothing.  If there was a serious discrepancy in your airmanship which required a 709 ride to verify improvement on your part, it's going to depend on whether it was a one time event or a trend in airmanship deficiency resulting in the check ride.  In addition have there been further reports of deficiency in your airmanship after the 709 ride?  That will also have an effect on an employer's judgment of you as a potential employee.
Whatever the reasons for the 709 ride, an employer is going to see it, so be prepared to explain anything associated with it.  
Look at this from the employer's perspective:  I'm going to put you in charge of a big, heavy multimillion dollar machine that you are going to pilot several miles off the ground at speeds close to that of sound.  If anything goes wrong, you're going to get killed, someone else on board is going to get killed, people on the ground are going to get killed and I'm going to get sued, go bankrupt, end up in jail, or all three if your negligence can be traced back to me.  Is there anything in your background which make me suspicious this is likely to happen if you are in my employ as a pilot?
The fact that you do make mistakes, possibly even serious ones, is not necessarily the issue here; everybody makes mistakes.  The last time you flew on an airliner the flight crew probably screwed something up.  People with thousands of PIC hours learn something new on their next flight and it's a mark of a good pilot that you can identify your own faults and fix them.  The Blue Angels have a private saying amongst themselves that "We've never flown a perfect airshow and we probably never will.  But we strive for the perfect airshow each and every flight".  Striving for perfection as a personal motivator is the mark of a good airman and looks good on a resume, no matter how balls up some flight in your logbook was.
The real issue here is do you have a recent or chronic history of uncorrected gross negligence or inability to handle the kinds of aircraft a potential employer flies which raises red flags as to your airmanship or trustworthiness.  If you have a spotty record or recent 709 ride in your recent past, take a couple of years staying on with your current employer and do an outstanding job.  Work on your airmanship and develop a stellar reputation with them as a pilot.  That will go a long way to erasing the past, or at least mute its bite.
Speaking of trustworthiness, DO NOT LIE TO A PROSPECTIVE EMPLOYER ABOUT A 709 RIDE OR ANY OTHER FAILED CHECKRIDE.  Aviation is built upon an honor system and any kind of detected lying or deceitfulness on your part is an automatic fail with no second chances, no matter how squeaky clean your career is up to that point.  If they ask about it, tell it like it was, no more, no less, and let the chips fall where they may.  It will yield the best possible outcomes, even if you don't get the job.

A:

A 49 U.S.C. 44709 ride is typically given when the FAA has reason to believe the applicant does not have the minimum pilot standards for their certificate or rating.  
As Pondlife pointed out, this can be because of a deficiency with the DPE that administered the practical test or because of an accident or incident after you passed the practical test.  It is also quite possible to get a 709 ride when you have broken the regulations, airspace infractions or other procedural things.  Typically the FAA will mitigate this risk with their compliance philosophy where they want to help weaker pilots maintain and improve their piloting capabilities.
I agree with Carlo that most airlines will see the 709 ride and ask questions.  How you respond to those questions will determine your aviation career.  

