Lipid membranes are crucial structures in cells, composed of a bilayer of lipids, membrane associated proteins, and many other molecules. There is increasing evidence that membranes and lipids have important bioactive roles in many cellular processes. The thin, soft, dynamic, and chemically complex structure of lipid bilayers makes their characterization difficult. Atomistic molecular dynamics computer simulations have provided valuable insight into the structure and dynamics of model membrane systems. I used MD simulations to study free energies of lipids in various model membranes. The method of umbrella sampling was used to calculate the free energy for moving a single lipid from water to the center of a lipid bilayer. From these calculations, we have determined the free energy barrier for lipid flip-flop, and the free energy for lipid desorption. Phospholipids with relatively large and zwitterionic head groups were shown to translocate in a pore-mediated mechanism, whereas ceramide, cholesterol, and diacylglycerol with small polar head groups crossed in a solubility-diffusion mechanism. The presence of cholesterol in membranes increased the free energy barrier for DPPC flip-flop, cholesterol flip-flop, and pore formation. For different membranes, we calculate the free energy difference of a lipid monomer in the bilayer compared to bulk water, which is the excess chemical potential for the lipid monomer in that environment. We found that cholesterol prefers more ordered and rigid lipid bilayers, while DPPC had a lower excess chemical potential in a pure DPPC bilayer compared to a DPPC bilayer with 40 mol% cholesterol. Neither ceramide nor diacylglycerol had a strong preference for a model lipid raft bilayer, compared to a POPC bilayer, while cholesterol did have a large preference for the raft bilayer. This work expands our understanding of lipid membranes.