Measurements of anisotropic flow coefficients (v_{n}) and their cross-correlations using two- and multiparticle cumulant methods are reported in collisions of pp at sqrt[s]=13 TeV, p-Pb at a center-of-mass energy per nucleon pair sqrt[s_{NN}]=5.02 TeV, Xe-Xe at sqrt[s_{NN}]=5.44 TeV, and Pb-Pb at sqrt[s_{NN}]=5.02 TeV recorded with the ALICE detector. The multiplicity dependence of v_{n} is studied in a very wide range from 20 to 3000 particles produced in the midrapidity region |η|<0.8 for the transverse momentum range 0.2<p_{T}<3.0 GeV/c. An ordering of the coefficients v_{2}>v_{3}>v_{4} is found in pp and p-Pb collisions, similar to that seen in large collision systems, while a weak v_{2} multiplicity dependence is observed relative to nucleus-nucleus collisions in the same multiplicity range. Using a novel subevent method, v_{2} measured with four-particle cumulants is found to be compatible with that from six-particle cumulants in pp and p-Pb collisions. The magnitude of the correlation between v_{n}^{2} and v_{m}^{2}, evaluated with the symmetric cumulants SC(m,n) is observed to be positive at all multiplicities for v_{2} and v_{4}, while for v_{2} and v_{3} it is negative and changes sign for multiplicities below 100, which may indicate a different v_{n} fluctuation pattern in this multiplicity range. The observed long-range multiparticle azimuthal correlations in high multiplicity pp and p-Pb collisions can neither be described by pythia 8 nor by impact-parameter-Glasma, music, and ultrarelativistic quantum molecular dynamics model calculations, and hence, provide new insights into the understanding of collective effects in small collision systems.