The observed toroidal rotation in Alcator C-Mod Ohmic L-mode plasmas has been found to depend strongly on the magnetic configuration. For standard discharges with a lower single null and the ion B x del B drift downward, and with B-T = 5.4 T, I-P = 0. 8 MA and n(e) = 1.4 x 10(20) m(-3), the core toroidal rotation is measured to be in the range of 10-20 km s(-1) (counter-current). Similar plasmas with upper single null (USN) have significantly stronger counter-current rotation, in the range 30-50 km s(-1). The rotation depends very sensitively on the distance between the primary and secondary separatrices in near double null plasmas, with changes of similar to 25 km s(-1) occurring over a variation of a few millimetres in this distance. Application of ICRF power has been found to increase the rotation in the co-current direction. The transition to H-mode is seen to occur in these standard plasmas when the core rotation reaches a characteristic value, near 0 km s(-1); hence higher input power is needed to induce the transition in the USN configuration.