Twenty-four galaxies with rings or partial rings were studied in the GEMS and GOODS fields out to z similar to 1.4. Most resemble local collisional ring galaxies in morphology, size, and clumpy star formation. Clump ages range from 10(8) to 10(9) yr, and clump masses go up to several x 10(8)M(circle dot), based on color evolution models. The clump ages are consistent with the expected lifetimes of ring structures if they are formed by collisions. Fifteen other galaxies that resemble the arcs in partial ring galaxies but have no evident disk emission were also studied. Their clumps have bluer colors at all redshifts compared to the clumps in the ring and partial ring sample, and their clump ages are younger than in rings and partial rings by a factor of similar to 10. In most respects, they resemble chain galaxies except for their curvature; we refer to them as "bent chains.'' Several rings are symmetric with centered nuclei and no obvious companions. They could be outer Lindblad resonance rings, although some have no obvious bars or spirals to drive them. If these symmetric cases are resonance rings, then they could be the precursors of modern resonance rings, which are only similar to 30% larger on average. This similarity in radius suggests that the driving pattern speed has not slowed by more by similar to 30% during the last similar to 7 Gyr. Those without bars could be examples of dissolved bars.