Will tsunami waves travel forever if there was no land? If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?
 A: The waves will not travel forever.
Water particles moving against and around each other will have friction, and the friction will cause motion energy to be converted to heat (which will dissipate throughout the water and air).  The wave will eventually cease to exist unless energy is added.
A: To answer this, I would appeal to the general principle which we call the 2nd law of thermodynamics. One way of expressing it is that the entropy of an isolated system cannot decrease. This means that in order to keep going for ever, a wave motion would have to involve no entropy increase. But almost all processes involve some increase of entropy, and in the case of water waves this is certainly going to happen, because of viscosity and turbulence in the water. Therefore the wave will gradually dissipate its energy and eventually die down. 
A: Waves keep going forever, in a way
As others pointed out already, waves tend to lose energy.
However, what will (theoretically) happen is that at any point in time the wave will lose a fraction of its energy, but never truely 100%. So though you will soon reach a point where random noise will make it practically impossible to detect a wave, the effect of the wave will never truely be gone.
So, while you will not notice it and definitely won't call it a tsunami, the wave can be seen as going on forever!
A: Of course, no. Tsunamis are a series of pressure waves with a longitudinal mode and have much higher wavelengths, speed, and period than the normal ones. Normal ocean waves only involve motion of the uppermost layer of the water, but Tsunami waves involve the movement of the entire water column from surface to seafloor. 
However, they are still akin to normal waves when it comes to dissipative forces such as friction between layers (or viscosity), just that it takes longer due to the sheer amount of energy density they carry. The mass of water getting displaced is particularly high, and due to high inertia, they tend to keep moving until resistance offered by the shape of the shoreline and other dissipative forces take over. Conservation of energy ensures the dissipation through heat, sound (which ultimately decays to thermal energy of the medium).
Tsunami waves have much longer periods ranging from 10 minutes to 2 hours, wavelengths of 100-500 km, and travel at speeds of 800-1000 km per hour[1]. Near the shore, the killer waves slow to between 10 to 20 mph (16 to 32 km/h) and gain enormous height. In reality, Tsunamis can travel as far as 10 miles (16 km) inland, depending on the shape and slope of the shoreline [2].
