So let's get started.
"Their formation is most often triggered by the water vapour in the exhaust of aircraft engines, but can also be triggered by the changes in air pressure in wingtip vortices or in the air over the entire wing surface. Like all clouds, contrails are made of water, in the form of a suspension of billions of liquid droplets or ice crystals. Depending on the temperature and humidity at the altitude the contrail forms, they may be visible for only a few seconds or minutes."
They can be very cool to see, but, from our admittedly limited research, seem to play a large part in why air travel is bad for the environment.
Basically, they cause something called radiative forcing, which is one of the causes of global warming. (They introduce energy into the atmosphere, which offsets the Earth's radiation balance. Just memorise that sentence.)
As for the flights that are most responsible for radiative forcing, the honour rests with night flights and winter flights. Wikipedia again:
"Other studies have determined that night flights are mostly responsible for the warming effect: while accounting for only 25% of daily air traffic, they contribute 60 to 80% of contrail radiative forcing. Similarly, winter flights account for only 22% of annual air traffic, but contribute half of the annual mean radiative forcing."
It's worth noting that contrails are only seen when airplanes are at cruising altitude. The scary/cool phenomenon of an airplane sending off what seems like a mini tornado during takeoff or landing is called wake turbulence. These can be found with great frequency in the Hertz Rental Car parking lot at LAX, where 747s fly overhead as they approach the runway, and vortices sometimes whip down alarmingly close to the cars. The first time I encountered one in this lot, I screamed for my friend to "Oh my God get in the car!" We slammed the doors shut, sat still with our pounding hearts, and then went to ask a Hertz employee, who laughed, and said, "It happens all the time!"
So, got it? Overhead, it's a contrail. At take-off and landing, it's called wake turbulence.