Imagine a line passing through the cores of two planets (in the same planetary system) and their star. Have we ever witnessed this - either with both planets on the same side of the star or on opposite sides? If so, was there a unique phenomenon associated with the event?
Referring to your #gravity tag this would only create a peak in the planets tidal forces. But this would be a visible effect in case the planets would be big and close enough... Last night happened that with Sun-Earth-Moon although they were not aligned as you say.
To sum up: a proper alignment would increase the effect of tidal forces.
There is no gravitational phenomenon associated with exact alignment. (moreover, exact alignment never happens, there is always a small deviation).
The directions of tidal forces are aligned and hence sum-up for alignment, but this maximum is quite broad and nothing spectacular happens near exact alignment.
You need close to exact alignment (depending on the sizes of the objects) to get an eclipse of one sort or another (a Solar complete eclipse is quite spectacular). This presumably requires the closest to exact alignment of all possible effects, but is not gravitational.
added in edit
If the planetary orbits were exactly co-planar, then exact alignment of the three bodies would occur regularly. However, the chance for the planetary orbits to be exactly (to infinite precision) co-planar is zero. This is just simple probability of continuous (as opposed to discrete) random variables: The probability density $p(x)$ for a continuous variable $x$ is finite, hence finding a value between $x$ and $x+\delta x$ has probability $p(x)\delta x$, which goes to zero as $\delta x\to0$. The chance of hitting close to exact alignment is the smaller the closer you want it to be.