We have studied the production of B hadrons in 1.8-TeV pp¯ collisions. We present measurements of the fragmentation fractions, fu, fd, fs, and fbaryon, of produced b quarks that yield B+, B0, B0s, and Λ¯0b hadrons. Reconstruction of five electron-charm final states yields fs/(fu+fd)=0.213±0.068 and fbaryon/(fu+fd)=0.118±0.042, assuming fu=fd. If all B hadrons produced in pp¯ collisions cascade to one of these four hadrons, we determine fu=fd=0.375±0.023, fs=0.160±0.044, and fbaryon=0.090±0.029. If we do not assume fu=fd, we find fd/fu=0.84±0.16.