Intro to Airbus
Updated: Jul 20, 2021

Airbus is an aeronautics company founded on December 18, 1970 in Blagnac, France. It has been for nearly 38 years in history. Nowadays, if you see an A-3## on the safety card in your seat pocket, you are on an Airbus. Airbus uses a side stick in the cockpit to control some movements of the plane. The five most popular Airbus aircraft are the A320, A330, A340, A350, and A380.
Purely out of interest, below is an mp4 file of the A330 taking off at full thrust. (TOGA at 0:31; rotation at 1:00)
(Special Note Ahead: The "You will experience it if" estimate also takes account of passenger bookings and aircraft availability. Airlines receive the number of passengers beforehand so they can arrange and dispatch aircrafts. )
A320 Family

The Airbus A320 is a narrow body, twin-engine airliner, first flown on February 22, 1987 with Air France. Its variants are A318, A319, and A321. As of now , over 10,000 A320s are built. It is one of the most successful airliners ever built, just behind the B737 in terms of the number of sales. Chances are you will board on an A320 on domestic flights or short distance flights.
Summary:
Narrow body airliner

Twin-engine
First flown on February 22, 1987 with Air France
Variants: A318, A319, A321, A321neo
Over 10,000 A320s
One of the most successful airliners ever in sales
You will experience it if: Domestic flights or short distance flights
A330 Family

The Airbus A330 is a wide body, twin-engine airliner first flown on November 2, 1992. Its variants are A330-200, A330-200F, A330-300, A330-900 (neo). Both the A330 and the A340 use tilted landing gears called bogies, shown in the picture. Around 1,500 A330's have been built. In nowadays, A330 has been used by most of the major airlines around the world. Chances are you will board on an A330 if it's an international flight ranging from 2 to 10 hours or from 3,110 to 8,350 miles.

Summary:
Wide body airliner
Twin-engine
First flown on November 2, 1992
Variants: A332, A332F, A333, and A330neo
A330 & A340 tilted landing gears: bogies
1,500 have been built
You will experience it if: long distance flights (3-10 hours; 3,110 to 8,350 miles)
A340 Family

The Airbus A340 is a wide body, four-engine airliner first flown on October 25, 1991. Its variants are A340-200, A340-300, A340-500, and A340-600. Both the A340 and the A330 use tilted landing gears called bogies, shown in the picture. A340s are not as popular as before because A330 has taken its place. Airbus found that using two engines (A330) are more efficient than using four engines (A340). Around 377 A340s are built in total, but only around 180 are in service. The largest operators are Lufthansa, South African Airways, and Iberia. The A340-600 is the longest airliner in the world with its length of 75.30 meters. Chances are you will board on an A340 if it's an international flight ranging from 6 to 13 hours. Nevertheless, it's pretty rare for you to get on an A340 in the present.
Summary:

Wide body airliner
Four-engine
First flown on October 25, 1991
Variants: A342, A343, A345, and A346
A340 & A330 tilted landing gears: bogies
Not very popular (taken over by A330)
Only around 377 A340s built; 180 in service
Largest Operators: Lufthansa, SAA, Iberia
World's longest in length: 75.30 meters
You will experience it if: long haul flights (pretty rare)
A350 Family XWB

The Airbus A350 is a wide body, twin-engine airliner first flown on June 14, 2013. Its variants are A350-800, A350-900, and A350-1000. Only around 331 A350s are built in total, and around 80 are currently in service. The largest operators are Qatar Airways, Singapore Airlines, and Cathay Pacific Airways. The A350 XWB is currently the newest Airbus aircraft family. Chances are you will board on an A350 if it's an international flight or a long haul flight.
Summary:

Wide body airliner
Twin-engine
First flown on June 14, 2013
Variants: A350-800/900/1000
Only around 331 A350s; 80 in service
Largest operators: Qatar, Singapore Airlines, Cathay Pacific
Newest Aircraft family currently
You will experience it if: international flights or long haul flights
A380-800

The Airbus A380-800 is a wide body, four-engine airliner first flown on April 27, 2005. Its variant is only itself, the A380-800. Only around 230 A380s are built in total. Just barely over the B747, the A380-800 has a cruising speed of around 650mph, making it the fastest airliner among Airbus and Boeing. It is also the biggest airliner in the world with a double decker. Chances are you will board on an A380 if it's an international flight or a very long haul flight (e.g. Taipei to Dubai).
Special Note: In 2019, Airbus announced that they will cease production of the A380 in 2021 due to weak sales. The Superjumbo jet's service of nearly 15 years has marked down one of the most influential era of wide-body jet. Its legacy will never be forgotten in the field of aviation.
Summary:

Wide body airliner
Four-engine
First flown on April 27, 2005
Variants: A388 (itself)
Only around 230 A380s
Has a cruising speed of 650mph, fastest among all Airbus and Boeing jets
Biggest airliner in the world (double decker)
Will end production in 2019
You will experience it if: international flights or very long haul flights (e.g. Taipei to Dubai)