We report the discovery of new Herbig-Haro shocks in the southeastern portion of the Taurus molecular cloud complex. The embedded protostar IRAS04325+2402, located in the eastern end of the B18 dark cloud in the cloud region known as L1535, drives a parsec-scale outflow with a length of at least 134' (5.5 pc) toward P.A. = 17°/197° making this the largest protostellar outflow found thus far in Taurus. The southern terminus of this flow located about 65' (~2.7 pc) from the IRAS source consists of a large previously discovered shock, HH 434-436. The northern lobe contains three faint shocks with the most distant being HH 696 located 2.8 pc north of the source. Two smaller shocks, HH 699 and HH 703, are found midway between the IRAS source and HH 434-436. HH 703 has a proper motion of 170 ± 30 km s-1 toward P.A. = 195° ± 10°. Additionally, we report the discovery of a dozen new Herbig-Haro objects tracing outflows and protostellar jets in B18 and near IC 2087, at least two of which have also attained parsec-scale dimensions. These observations demonstrate that some low-mass stars forming from the Taurus clouds drive giant flows which can excite shocks in the inter-cloud medium degrees from their sources, providing further evidence for the generation of large-scale mass motions and turbulence by protostellar outflows.