Why do some fighter jets have two vertical tails and some only one?

Why do some fighters have only one vertical stabilizer, while most modern fighters have two?

In most, if not all, modern fighters with twin vertical tails, the vertical tails are smaller than those on fighters with single vertical tails. The major exception to this rule is the F-22 Raptor, where both vertical tails are large. In fact, we should call the vertical tail a vertical tail wing, but for brevity and clarity we will use the term vertical tail.

Aircraft use their vertical tail for yaw input, which makes them more aerodynamically acrobatic than if they had no vertical tail.

Schematic view of the F-18 Hornet with projections of the X, Y and Z axes...

The vortex created by the wing leading edge of the F-22.

The F-18, F-22, F-35 and several other aircraft have vertical tails that slope outward. They make special use of the vortex created by the elongated and exaggerated wing leading edge.

Extended vortex formation in the twin vertical tails of the F-35.

Other twin vertical tail aircraft, such as the SU-27, F-15 and others, use straight vertical tails. These use the air from the leading edge in a different way, so the twin vertical tails help with the extra maneuverability of the aircraft.

Most aircraft with twin vertical tails have twin engines, the F-35 Lightning II being the exception.

Most vertical single-tail jets such as the F-16, Eurofighter Typhoon and Rafale are built in smaller airframes than vertical twin-tail aircraft such as the F-15, F-14, F-18, Su-27. 

The F-16 is a small, single-engine aircraft, but it is a very powerful jet, aerodynamically very robust. The reason it can make the most of a single vertical tail is its size and power-to-weight ratio. In the world of jets, the F-16 is the athlete of the sky.

The F-16's wing vortices (vortex).

Eurofighter Typhoon wing vortices and canards.

Then come the single vertical-tail jets, which have not only a single vertical tail, but also twin engines and twin canards. Canards are an excellent addition to a single vertical-tail jet. They help with the lift, agility and aerodynamics of a fast jet. The Eurofighter Typhoon, the backbone of the UK, German, Italian and Spanish Air forces and sold to customers such as Austria, Saudi Arabia, Kuwait, Oman and Qatar, is a shining example.

Canards assist the horizontal tail (horizontal stabilizer) to keep the aircraft moving in the vertical (pitch) axis and the wings to avoid too much stress in lift. An airplane with canards can easily carry its own weight and more, while an airplane without canards may have difficulty lifting and carrying its own weight.

The only problem with canards assisting the wings and horizontal tail is controllability at stall speeds. To compensate for this, designers and engineers design and build the aircraft in such a way as to make it almost impossible for the pilot to fly it without computer assistance. Every action and input from the pilot goes to the computers that control the fly-by-wire system. This is what makes the 4.5th generation Eurofighter Typhoon, for example, so agile.

Eurofighter Typhoon

Conclusion

Double-vertical-tail and single-vertical-tail jets are designed to use the air generated around the aircraft in different ways to make the aircraft competitive in aerodynamic agility.