We present results on 12 X-ray bright clusters observed at 1.4 GHz with the Green Bank Telescope. After subtraction of point sources, we reach a median (best) 1-sigma noise level of 0.01 (0.006) microJy/sq. arcsec, and find a significant excess of di
ffuse, low surface brightness emission in 11 of 12 clusters. We present initial 1.4 GHz Very Large Array results on Abell 2319. We find: (a) four new detections tentatively classified as two halos (A2065, A2069) and two relics (A2067, A2073); (b) the first detection of the radio halo in A2061 at 1.4 GHz, making it a possible ultra-steep spectrum halo (alpha ~ 1.8); (c) a ~2 Mpc radio halo in the sloshing, minor-merger cluster A2142; (d) a >2x increase of the giant radio halo extent and luminosity in A2319; (e) a ~7x increase to the integrated radio flux and >4x increase to the observed extent of the peripheral, polarized radio relic in A1367 to ~600 kpc; (f) significant excess emission of ambiguous nature in three clusters. Our radio halo detections agree with the well-known X-ray/radio luminosity correlation, but are larger and fainter than expected. The volume averaged synchrotron emissivities are 1-2 orders of magnitude below the previous characteristic values. Some of the halo-like detections may represent previously unseen, very low surface brightness emission or blends of shock structures and sub-Mpc scale turbulent regions. Four of the five tentative halos contain one or more X-ray cold fronts, suggesting a possible connection between gas sloshing and particle acceleration on large scales. We see evidence for a possible inter-cluster filament between A2061 and A2067. For our faintest detections, we note the possibility of residual contamination from faint radio galaxies. We also quantify the sensitivity of the NVSS to extended emission as a function of angular size.[abridged]
