More precisely, every singularity of finite type over $\mathbb{Z}$ (up to smooth parameters) appears on the Hilbert scheme of curves in projective space, and the moduli spaces of: smooth projective general-type surfaces (or higher-dimensional varieties), plane curves with nodes and cusps, stable sheaves, isolated threefold singularities, and more. The objects themselves are not pathological, and are in fact as nice as can be: the curves are smooth, the surfaces have very ample canonical bundle, the stable sheaves are torsion of rank 1, the singularities are normal and Cohen-Macaulay, etc.
Thus one can construct a smooth curve in projective space whose deformation space has any given number of components, each with any given singularity type, with any given non-reduced behavior along various associated subschemes. Similarly one can give a surface over $\mathbb{F}_p$ that lifts to $p^7$ but not $p^8$. (Of course the results hold in the holomorphic category as well.)