We present observations of the three-dimensional velocity distributions of protons in the energy range 20 eV to 52 keV at locations within and near the current sheet of Earth's magnetotail at geocentric radial distances 35 to 87 RE. These measurements were acquired on December 8, 1990, with a set of electrostatic analyzers on board the Galileo spacecraft during its approach to Earth in order to obtain one of its gravitational assists to Jupiter. It is found that the velocity distributions are inadequately described as quasi-Maxwellian distributions such as those found in the central plasma sheet at positions nearer to Earth. Instead the proton velocity distributions can be categorized into two major types. The first type is the ''lima bean'' shaped distribution with high-speed bulk flows and high temperatures that are similar to those found nearer to Earth in the plasma sheet boundary layer. The second type consists of colder protons with considerably lesser bulk flow speeds. Examples of velocity distributions are given for the plasma mantle, a region near the magnetic neutral line, positions earthward and tailward of the neutral line, and the plasma sheet boundary layer. At positions near the neutral line, only complex velocity distributions consisting of the colder protons are found, whereas both of the above types of distributions are found in and near the current sheet at earthward and tailward locations. Bulk flows are directed generally earthward and tailward at positions earthward and tailward of the neutral line, respectively. Only the high-speed, hot distribution is present in the plasma sheet boundary layer. The observations are interpreted in terms of the nonadiabatic acceleration of protons that flow into the current sheet from the plasma mantle. For this interpretation the hot, ''lima bean'' shaped distributions are associated with meandering, or Speiser, orbits in the current sheet. It is suggested that the colder, lower-speed proton velocity distributions are the result of fractional or few gyromotions before ejection out of the current sheet, but this speculation must be further investigated with appropriate kinetic simulation of trajectories.