We experimentally investigate the nonlinear optical pulse dynamics of ultrashort laser pulses propagating in gas-filled hollow capillary fibers in different dispersion regimes, which are achieved by tuning the gas pressure. When the pulse propagates in the anomalous dispersion regime we observe soliton dynamics accompanied with soliton-plasma effects, such as self-compression, resonant dispersive-wave emission in the fundamental as well as in higher-order modes, soliton blueshifting, and ionization-induced pulse splitting. Propagation of the pulse in the vicinity of the zero-dispersion wavelength results in pulse splitting and subsequent cross-phase modulation leading to the generation of an additional frequency-shifted band and a three-octave broad supercontinuum. In the case of pulses propagating in normal dispersion we observe the generation of a broad and flat supercontinuum. In this regime, the experimental results are less well described by simulations that consider only the propagation dynamics inside the fiber. Free-space simulations of the beam propagation in the bulk gas, before the capillary entrance, suggest that this discrepancy is caused by self-focusing and ionization altering the pulse spatial and temporal shape, affecting both the coupling efficiency and the subsequent propagation inside the capillary.