The circular cylinder has been the generic geometry employed to understand many aspects of flows around bluff bodies, including the transition to a turbulent wake flow. The FLAIR group has been interested in the types and orders of instabilities and transitions for a range of bluff body flows. In this paper, variations of the flow from the generic case of a fixed circular cylinder are considered: contraction to a thin plate whilst preserving elliptical profile; elongation of cylinders with elliptical leading edge and square trailing edge: contraction of tori from large major radius to a sphere; and transverse oscillation of a circular cylinder. For elongated cylinders with streamlined leading edges, the analogs of the instability modes for a circular cylinder become unstable in the reverse order. As well, the analogue of mode B has a significantly increased relative spanwise wavelength and appears to have a different near-wake structure. At the other extreme, for a normal flat plate, the wake first becomes unstable to a non-periodic mode that appears distinct from either of the dominant circular cylinder wake modes. For tori, which have a local geometry approaching a two-dimensional circular cylinder for large aspect ratios, the sequence of transitions with increasing Reynolds number is a strong function of aspect ratio. For intermediate aspect ratios, the first occurring wake instability mode is a subharmonic mode. In the case of transversely oscillating cylinders, it is shown that when the two-dimensional wake is in the 2S configuration, modes A, B and QP are present, similar in nature and symmetry structure to the modes of the same names for a fixed cylinder. However, increasing the amplitude of oscillation sees the critical Reynolds number for mode A increase significantly, to the point where mode B becomes critical before mode A. For higher Reynolds numbers, the two-dimensional wake loses its spatio-temporal symmetry and takes on the P + S configuration. With the onset of this configuration, modes A, B and QP cease to exist. It is shown that two new three-dimensional modes (SL and SS) arise from this base flow. The variety of transition modes and order of transition for these different cases may have implications for the route to wake turbulence for such bodies, distinct from that found for a fixed circular cylinder.