Ideal airflow across an airplane especially is called laminar. In laminar airflow, the air moves from front to back smoothly clinging to the airframe along its whole length.
If you can't get laminar airflow, the next best condition is a turbulent airflow that doesn't separate from the airframe. This isn't as good as laminar as it generates some additional drag in creating the turbulent condition.
The condition that designers want to avoid, as much as possible, is airflow separation from the airframe. What can happen is the airflow separates from the airframe and creates a negative pressure area that draws in airflow that goes forward instead of aft. This separation and reverse flow generates a considerable increase in drag and on flight controls reduces their effectivity to varying amounts depending on the amount of reverse airflow.
Generally, at each airframe's design point, the airflow is as smooth as possible and generally going from front to rear.
When an airplane is operated at speeds and altitudes that differ from the design point (for instance; take-offs, approaches, landings) you get an increase in airflow separation and reverse airflow. Vortex generators are one method (that is favored by Boeing) to restore a turbulent (vortex) airflow that is going front to rear. The vortex generator produces a small vortex (or spinning cone of air), since the vortex increases in diameter as it flows, horizontally from the generator, contact with the airframe is maintained and the flow is generally front to rear.
Douglas design teams prefer strakes and vortilerons in place of vortex generators. On the leading edge of all DC-9/MD-80/MD-90/717 airplanes is a forward pointing fairing that extends beyond the lower leading edge of the wing at about 1/3 of the span and in line with the horizontal stabilizer. It is called a vortileron and it generates a vortex that, at higher angles of attack, the vortex passes over the horizontal stabilizer increasing the efficiency of the stabilizer and elevator during low speed flight.
Douglas has strakes on engine cowls (MD-80's, MD-90's), fuselage noses (DC-9-50, MD-80, MD-90), on engine cowls (DC-8-72's and -73's, DC-10, MD-11).
The Beech 1900D is stake city, with them installed on the forward fuselage, rear fuselage, and underside of the horizontal stabilizer.
An unintended vortex generator that arose in NASCAR racing is the fairing on the top of the car roof just behind the windshield. This fairing is used to contain one of the in-car tv cameras and it was found that some body styles received an aerodynamic benefit from the fairing, where other didn't. NASCAR's solution was to put the fairing on all cars, whether they had a camera in it or not. F1 cars have a aerodynamic Tee on top of the roll bar that is also used for an in-car camera and it probably provides a vortex that increases the rear wing efficiency. All cars have the Tee, but they don't all have cameras.