Why can't liquids oppose tangential forces acting on them? 
Also, when a glass of water is inclined at a certain angle, why does the surface of water continue to remain parallel to ground? 
 A: Liquids actually can oppose tangential forces acting on them because of their property of viscosity.  But, in order for them to be able to do this, they have to be deforming (with time).  In the situation you have depicted, the fluid is in hydrostatic equilibrium, so it is not deforming.  Therefore, the shear stresses at its boundaries (as well as throughout the fluid) are zero.
A: Liquids do oppose tangential forces acting on them, this is what viscosity measures. Viscosity is the property of a liquid (or any fluid) which opposes the relative motion between two surfaces of the liquid that are moving at different velocities and it is caused by friction between the molecules of the liquid. In other words, it measures the resistance of a liquid to deformation by shearing stress (a tangential force).
In the example you have mentioned, when a glass filled with a liquid is tilted, let's look at the forces acting on the body if the liquid did not flow such that the surface remained parallel to the ground:

In this stage, the potential energy due to gravity of the body is greater than if the surface of the liquid were parallel to the ground. For this reason, the liquid would tend to attain the state that is depicted in the picture you have uploaded.
What I think you were asking is why the adhesive forces do not prevent the liquid surface from remaining parallel to the ground. I am not an expert in the field of fluid mechanics, so take my answer with a grain of salt. If you were to tilt a glass of honey, for example, you would see that the liquid doesn't reach that "parallel state" as fast (I may test this and upload a photo later for reference). The adhesive force between the glass and the honey and the viscosity of honey is large enough (the viscosity of honey ranges from 10,000 cP to 12,000 cP) to counteract the energy difference between the tilted surface and the parallel surface for a minimum amount of time.
In the liquid in the picture (it looks like orange juice to me, which has properties similar to water), the adhesive and viscous forces are present; they are just not large enough to counteract the force of gravity on the liquid (the viscosity of orange juice is approximately 5 cP).
A: The answers by Chester Miller and Abhimanyu Sinha are applicable to Newtonian fluids. A Newtonian fluid cannot resist tangential forces when it is at rest, but only when it is already flowing. In other words, in a Newtonian fluid, tangential stress is set up due to rate of change in strain and not the strain itself.
Elastic solids on the other hand develop tangential stresses due to strain itself. There exists a continuous spectrum from Newtonian-fluids to elastic-solids, in which the material displays characteristics of both fluids and (elastic) solids. That material in which fluid behaviour is dominant is called a viscoelasitc fluid. In a viscoelastic fluid tangential stresses are set up due to strain as well as due to strain-rate. Polymer solutions (used in plastic manufacture), pitch, etc. are examples of viscoelastic fluids. However viscoelastic fluids have a finite memory in the sense that if their deformation is maintained over a long enough time (compared to their molecular relaxation time scale) then they forget about their deformation (or strain) history and behave like Newtonian fluids. See this video, especially at 5:45, to see a viscoelastic fluid behaving like an elastic solid over short enough time that it remembers its strain history.
A: If it could oppose tangential forces indefinitely, then you wouldn't call it a liquid. The very definition of a liquid is a substance that deforms to fill up available horizontal space.
The viscosity of liquids does cause non-indefinite opposition against tangential forces, although not forever. Thick liquids like honey are still liquids.
But when you have "liquids" being so thick that they take ages to deform - or that only deform under certain conditions, such as under pressure - we tend to not call them liquids anymore although they also aren't solids (such as tooth-paste and wet beach sand).
