Annexins are a family of proteins characterized by their ability to bind anionic membranes in response to Ca2+-activation. They are involved in a multitude of cellular functions including vesiculation and membrane repair. Here, we investigate the effect of nine annexins (ANXA1-ANXA7, ANXA11, ANXA13) on negatively charged double supported membrane patches with free edges. We find that annexin members can be classified according to the membrane morphology they induce and matching a dendrogam of the annexin family based on full amino acid sequences. ANXA1 and ANXA2 induce membrane folding and blebbing initiated from membrane structural defects inside patches while ANXA6 induces membrane folding originating both from defects and from the membrane edges. ANXA4 and ANXA5 induce cooperative roll-up of the membrane starting from free edges, producing large rolls. In contrast, ANXA3 and ANXA13 roll the membrane in a fragmented manner producing multiple thin rolls. In addition to rolling, ANXA7 and ANXA11 are characterized by their ability to form fluid lenses localized between the membrane leaflets. A shared feature necessary for generating these morphologies is the ability to induce membrane curvature on free edged anionic membranes. Consequently, induction of membrane curvature may be a significant property of the annexin protein family that is important for their function.