We present the result of our accurate measurements of the a- and b-axis resistivity (rho_a and rho_b), magnetoconductivity (Deltasigma / sigma), Hall coefficient R_H, and the a-axis thermopower S_a in untwinned YBa_{2}Cu_{3}O_{y} single crystals in a wide range of doping (6.45 < y < 7.0). The systematics of our data reveals a number of novel 60-K-phase anomalies in the charge transport: (i) Temperature dependences of rho_a show anomalous overlap below ~130 K for 6.65 < y < 6.80, (ii) Hall mobility mu_H shows an enhancement near y ~ 6.65, which is reflected in an anomalous y dependence of sigma_{xy}, (iii) With decreasing temperature R_H shows a marked drop upon approaching T_c only in samples with 6.70 < y < 6.85, (iv) Superconducting fluctuation magnetoconductivity is anomalously enhanced near y ~ 6.7, and (v) H_{c2} is anomalously reduced near y ~ 6.70. We discuss that the fluctuating charge stripes might be responsible for these anomalies in the charge transport.