We present K-band (2.2 m) imaging polarimetry that resolves 19 T Tauri binary and multiple systems in the Taurus-Auriga and Scorpius-Ophiuchus star-forming regions. We observed systems with projected separations 1B5-7B2 ($200-1000 AU) in order to determine the relative orientation of the circumstellar disks in each binary system. Scattered light from these disks is polarized, allowing us to deduce the position angle of the disk on the sky from the position angle of polarization even though our observations do not resolve the disks themselves. We detected measurable polarization (typically 0.5%-2%, with typical uncertainty 0.1%) from both stars in 14 of the systems observed. In eight of the nine binary systems, the two stars' polarization position angles are within 30 of each other, inconsistent with random orientations. In contrast, the five triple and quadruple systems appear to have random disk orientations when comparing the polarization position angles of the widest pair in the system; the close pairs are unresolved in all but one system. Our observations suggest that disks in wide (200-1000 AU) binaries are aligned with each other within P20 but not perfectly coplanar. However, we cannot conclusively rule out random relative disk orientations if the observed polarizations are significantly contaminated by interstellar polarization. Even in the presence of interstellar polarization our observations securely exclude coplanar disks. These results provide constraints on possible binary formation mechanisms if the observed orientations are primordial. On the other hand, models of disk-binary interactions indicate that the disks may have had time to decrease their relative inclinations since formation. If the common orientation of the disks in these binaries is a tracer of the binary orbital plane, then our results also have significance for the stability of planetary orbits, suggesting that planetary systems in wide binaries should be stable over 10 9 yr timescales.