An interlock connector (10) for interlocking stackable building blocks (26). The blocks are provided with apertures (32), such as grooves, on their top and bottom surfaces. The connector comprises a main body which includes two separate and vertically superimposed body portions and is interposed between two stacked blocks with each body portion disposed in a respective groove (32). One body portion is pivotable with respect to another, with a vertical pivot axis that is offset from the central vertical axis of the main body, so as to be pivotable to positions where the stacked blocks are offset. In another embodiment, the interlock connector comprises a single piece main body having an aperture to receive a projection protruding from the surface of one of the stacked blocks while being disposed in the groove of the other block, with the connector being pivotable about the projection to positions where the stacked blocks are offset. Other embodiments include connectors with offset upper and lower body portions to interlock blocks having symmetrical grooves, wherein certain of the embodiments allow a block to be pivoted about a body portion.