Is there a theoretical limit for energy density? How much energy can be added to a small volume of space? Perhaps like the focal point of a very high power femtosecond laser for a short time, or are there other examples like the insides of neutron stars that might be the highest possible energy density? Is there any fundamental limit?
 A: This limit is given by the Bekenstein Bound. It is proportional to the surface area of the surface enclosing a given volume. Exceeding this bound would create a black hole.
A: There is a limit to how much energy that can be contained in a finite volume, after which the energy density becomes so high that the region collapses into a black hole.
We also know that matter and energy are equivalent according to the Einstein equation $$E=mc^2\tag1$$ So if we can determine the greatest amount of matter that can fit into a volume just before it collapses into a black hole, the corresponding energy should also indicate the greatest energy confined in the volume just before it becomes a black hole.
The maximum amount of matter, mass $M$, that can be contained in a given volume before it collapses into a black hole, is given by the Schwarzschild radius $$r_s=\frac{2GM}{c^2}\tag2$$ Using (1) we can then write $$M=\frac{E}{c^2}$$ so that equation (2) becomes $$r_s=\frac{2GE}{c^4}$$ or $$E=\frac{r_sc^4}{2G}$$
Note that this is still energy, and to get to energy density we need to define the volume which is of course $$V=\frac 43 \pi r_s^3$$ so that the energy density is $$\epsilon =\frac{3c^4}{8\pi Gr_s^2}$$
This computation is based on not much more than the equivalence of matter and energy. It represents a bound on the maximum amount of matter, and therefore energy, in a spherical volume of radius $r_s$ before the volume  containing the matter collapses into a singularity, which of course has no properly defined volume.
