Thanks to Boris Tsirelson, we know that not all infinite-dimensional Banach spaces contain either $c_0$ or $\ell_p$ for some $p\in [1,\infty)$. But all known counterexamples are constructed in a particular inductive way, and all spaces that "occur in nature" do contain $c_0$ or $\ell_p$, sometimes (as in the case of Orlicz spaces) for non-trivial reasons.