There are actually several different "limits" one might encounter. The one everyone talks about is not fusing past iron. This comes from the fact that isotopes in the vicinity of ${}^{56}\mathrm{Fe}$ consist of the most tightly bound nuclei. See Wikipedia for a discussion and some binding energy curves. If you are interested in why there is a peak, it comes from balancing various energetic considerations, and you can glean some understanding from the semi-empirical mass formula and associated liquid drop model of the nucleus. Keep in mind this is an empirical fit to a somewhat justified simplification - it does not encompass all we know about nuclear forces and such. Once a star has fused nucleons into these isotopes, energy can no longer be extracted from further fusion. As a result, stable, sustainable nuclear burning has come to an end.
However, a star may never reach this point. In general, stars go through several different phases of life, characterized by what nuclear fuel they burn. The (greatly oversimplified) story is something like
$$ {}^1\mathrm{H} \to {}^4\mathrm{He} \to {}^{12}\mathrm{C}, {}^{16}\mathrm{O} \to \ldots \to {}^{56}\mathrm{Fe}. $$
As one fuel runs out, the star (or at least its core) shrinks and heats up, enabling fusion of heavier elements. Our Sun won't get very far past the helium stage; it simply does not have enough mass.
On the other hand, very massive stars don't stop at iron and nickel and such things. Just because a reaction is endothermic does not mean it cannot happen. In core-collapse supernovae, their violent death causes heavier elements to be created. A good deal of this is accomplished with neutron (or alpha, if any helium is to be found) capture, so it is fusion, but only in the sense of unequal mass things colliding. This sort of process can produce just about any heavy element in the universe, with things past about uranium undergoing spontaneous fission too quickly to gain a foothold in cosmic abundances.