Normally we would assume that BeCl2 would be sp hybridized; the beryllium only has two electrons to share, and the chlorines each need only one, so this should demand a total of two bonds, which is satisfied by sp hybridization. However, in reality, the solid state of BeCl2 involves donation of a pair of electrons from the chlorines to a neighboring BeCl2 molecule at a 45 degree angle, forming a pair of coordination bonds with the central beryllium of each. This means each beryllium is experiencing four bonds, which require that it be sp3 hybridized. If you could somehow isolate a single molecule of solid-state beryllium chloride, then it should have an sp hybridization.
In the gaseous phase, beryllium chloride exists in equilibrium as two compounds; the linear BeCl2 (which is sp hybridized, as previously mentioned) and a dimerized form; (BeCl2)2, where each beryllium is bound to three chlorines, which requires that the hybridization is sp2. Above 1200K, the dimers dissociate, leaving only the linear structure.