Our recent experimental studies on the so-called 1/8 anomaly in the Bi-2212 and Y-123 phases and also on the new anomaly in the overdoped region of the La-214 phase are reviewed. In the partially Zn-substituted Bi-2212 and Y-123 phases, we have found anomalous suppression of superconductivity (SC) at p (the hole concentration per Cu in the Cu02 plane) ~ 1/8, and it has been found from the muon-spin-relaxation (/^SR) measurements that the magnetic correlation between Cu spins is enhanced singularly at p ~ 1/8. Furthermore, we have found giant suppression of SC singularly at x = 0.21 in the 1% Zn-substituted single-crystals of La2-xSr x Cui_ 1/ Zn 3/ 04 (LSCZO), and it has been found from the /xSR measurements that the magnetic correlation is also enhanced at x = 0.21. These results suggest that the dynamical stripe correlations of holes and spins exist in the Bi-2212 and Y-123 phases as well as in the La-214 phase and that they tend to be pinned by a small amount of Zn, leading to quasi-static stripe order and the suppression of SC at p ~ 1/8 in the Bi-2212, Y-123, La-214 phases and also at a; = 0.21 in LSCZO. If this tendency is the case in a wide range of p> it is possible to understand the universal experimental results in the high-T c cuprates that Zn is a strong scatterer in the unitarity limit and that the Zn substitution markedly suppresses SC.