We have investigated the proximity effect in superconductor/ferromagnet junctions in a systematic manner to discuss the relationship between the zero-energy peak (ZEP) of the local density of states (LDOS) and spin-triplet odd-frequency pairing. By exactly solving the nonlinear Usadel equations, we have found that the ZEP is realized in a wide range of geometrical and material parameters in the case of the noncollinear magnetization. This strongly suggests the robustness of the ZEP induced by spin-triplet odd-frequency pairing in such systems. We also found that the crossover from singlet pairing to triplet pairing can be detected by measuring the F layer thickness dependence of the ZEP height. Furthermore, we show how to observe signatures of spin-triplet odd-frequency pairing and the pairing crossover by LDOS measurement. Our results provide a direct way to experimentally detect signatures of the odd-frequency pairing state.