The main reason for using the prism here is to provide the evanescent field (via the total internal reflection, TIR) that excites plasmons in a metal film that is coated on a base of the prim.

Serge

Thanks Serge for your answer, however let me see if I understand, the metal/glass index refraction ratio is indeed less than one to allow total reflection to occur and thus provide the evanescent field. Howevver if you simply use a microscope slide and coat with a metal wouldn´t you have the same situation required for plasmon resonance? Maybe I am missing something?

In short, convenience and the ease of manipulation with light. Look at few nuances. You'd need to obtain the TIR at the glass/metal interface such that the evanescent field reaches the metal/air interface where the plasmon is excited (the thickness of the film is critical!). So, in the prism configuration the incident ray has a relatively small angle (relative to the normal to the side of the prism) so bending is minimal and TIR can be achieved (and monitored on the opposite side) under well controlled angles. Now imaging having a thin glass slide. Try to couple light from the bottom, vary the angle and see at what angle you can achieve (if it's possible) TIR. Then, you may need to cross the edge and go through the side of the glass-slide. If it's too thin, you'd need to have a thicker plate with polished sides. Again, work out the angles and see by yourself. The devil is in details:)     

It helps to couple the horizontal wave vector components of the incident light into the propagating SPP wave vector. The prism should have large refractive index, requiring also certain incident angle to match the two wave vectors. The film thickness plays an important role as explained above by Serge.

Instead of using the prism configuration, you can also use gratings to the couple the wave vector; however, the efficiency is much lower than using the prism with much scattering loss.

In other words - to provide proper synchronization between the SP wave vector and the available tangent component of the wave vector of the incidence light. 

While the primary reason to have a coupling element in SPR is really just an excitation of evanescent field which couples to surface plasmons (see answers above), there is a number of secondary reasons why this coupling element comes mostly in shape of (triangular) prism.

They are especially important for SPR imaging. The best optical conditions (least aberrations and back-reflections, best resolution, the intensity vs angle dependence in the illuminated spot) are achieved when the light beam falls in direction normal to the prism facet.  That's why you can see sometimes not just a typical 60° and 45/90° prisms, but also prisms with very finely defined geometries designed for specific application. Higher refractive index help too, for similar geometrical optics reasons.

Particularly interesting case is hemispherical prism (a plano-convex or half-ball lens, actually) - it facilitates the normal incidence angle of light ray on the facet, but other than that it is hardly usable for imaging purposes because the resulting incidence angle on the gold coated surface (correspondingly, SPR conditions ) will vary across the spot.

Application of other prism geometries (like thick glass block which was already mentioned above by Serge, rhomboids,  trapezoids  etc) is also possible, but they have many  drawbacks. Typically such geometries are applied to exploit some particular advantages  - like folding the light path, easing of angle or wavelength scanning etc.

Thank you for your answers, following shavkat comment I guess a semicylindrical prism will also work well.

A prism or a diffraction grating are needed because you need to match the momentum of the incident light to that of the surface polariton, i.e. the longitudinal oscillations along the surface. This is because of the dispersion relationship for surface plasmons in matter, i.e. the frequency of the surface polaritons is tied to the wave vector by the omega(kx) dispersion relationship.