That's a question that's often raised. Before answering it, I should try to clarify a bit what's happened so far.
The probing into deeper and deeper layers has not resulted in a cascade of ever more complicated ingredients. In some ways it's the opposite. The force laws governing these interactions have now been boiled down to two: the unified electroweak interaction and the quantum chromodynamic interaction. There's also gravity, important on different scales, and so far untouched by accelerator experiments. That's much simpler than the welter of different forces that show up in more superficial mechanics. That shower of new particles you describe turns out to require only a few new ingredients- six types of quarks. There is still some complication, in that a few dozen numbers are needed to describe the whole theory (various ratios of particle masses, etc.) but that's already a lot simpler than, say, the properties of about 100 elements.
There's very good reason to expect that with a bit more probing a single unified law for the electroweak and chromodynamic interactions will emerge. Perhaps an overall unified description including gravity will be developed, maybe along the lines being explored in string theory.
So far we've seen a few doll layers. First, full atoms. Second nuclei plus electrons. Third, protons and neutrons and electrons. Fourth, quarks and leptons. The only level that even superficially looked simpler than the current one was the 'protons, neutrons, electrons' level. However, since there was no good simplification for the interactions at that level, it was really more complex than where we are now. As for whether at some point there's an inmost doll, with nothing further inside, we don't know. If there is, we don't know if it will ever be reachable by our species. But why not give it a shot?
p.s. There's a beautiful discussion of exactly this issue in one chapter of The Character of Physical Law, by Richard Feynman.
(published on 03/02/09)