A comprehensive analysis of magnetic clouds observed by the Advanced Composition Explorer (ACE) spacecraft from February 1998 to July 2001 is presented. The magnetic field data from the MAG instrument is fit with the cylindrically symmetric, linear force-free model and the fit parameter distributions are examined. This magnetic field model enables us to map plasma data from the SWEPAM and SWICS instruments to a position within the model cylinder. A superposed epoch analysis of all our magnetic cloud events is used to construct diameter cuts through an average cloud profile in any desired plasma, elemental composition, or charge state quantity. These diameter cuts are found to have nontrivial structure and there appears to be significant composition and structural differences between clouds of different speeds. The slow magnetic clouds (⟨Vrad⟩ < 500 km/s) have an almost constant proton density profile whereas the fast magnetic cloud (⟨Vrad⟩ ≥ 500 km/s) profile is depleted throughout with symmetric dips and a local maximum at the cloud center. The fast magnetic clouds have a slightly higher Nα/Np ratio than the slow clouds. Both the fast and slow events have enhanced oxygen and iron charge states compared to the slow solar wind. The fast events have a slightly increased O7+/O6+ average profile and a much stronger Fe≥16+/Fetotal profile than the slow events. We briefly discuss the implications for physical conditions at the Sun, the role these coronal mass ejections (CMEs) may play in transporting magnetic flux, and the application of our structure results to the current flux rope CME modeling effort.