The dynamical evolution of H II, regions and wind-driven bubbles in dense clouds is studied. In particular, we address two different issues: (1) the conditions under which ultracompact H II) regions can reach pressure equilibrium with their surrounding medium (and thereby stall their expansion) and (2) the appearance of a powerful dynamic instability in expanding H II regions. At pressure equilibrium, the ionized regions become static, and as long as the ionization sources and the ambient gas densities remain about constant, the resulting UCHII regions are stable and long-lived. The equilibrium sizes and densities, R(S,eq) similar to 3 x 10(-2)F(48)(1/3)T(HII,4)(2/3)P(7)(-2/3) pc and n(i,eq) similar to 4 10(4)P(7)T(HII,4)(-1) cm(-3) (where F-48 is the photoionizing in units of 10(-7) dyne cm(-2), and T-HII,T-4 is the ion temperature in units of 10(4) K), are similar to those actually observed in UCHII regions. Similarly, ultracompact wind-driven bubbles can reach pressure equilibrium, and the resulting final sizes are similar to those of UCHII's. The same is true for a combined ultracompact structure consisting of an interior wind-driven cavity and an external HII region. For nonmoving stars in a constant-density medium, the lifetimes for all types of ultracompact objects only depend on the stellar lifetimes. For cases with a density gradient, depending on the core size and slope of the density distribution, some regions never reach the static equilibrium condition. A powerful dynamic instability appears when cooling is included in the neutral gas swept up by an HII region or a combined wind-II n region structure. This instability was first studied by Giuliani and is associated with the thin-shell instability described by Vishniac. The internal ionization front exacerbates the growth of the thin-shell instability, creating a rapid shell fragmentation, and our numerical simulations confirm the linear analysis of Giuliani. The fragments tend to merge as the evolution proceeds, creating dense and more massive clumps, and are slowly eroded by ionization fronts. Thus the resulting structures have a variety of shapes, sizes, densities, and lifetimes. Intriguing features such as ''elephant trunks'' and cometary-like globules can easily be explained as a result of this instability.