Results of a study of the exclusive semileptonic decay modes D0→K-e+νe and D+→K-π+e+νe are presented. We have measured their branching fractions relative to those of dominant hadronic modes, BF(D0→K-e+νe)/BF(D0→K-π+)=0.91±0.07 ±0.11 and BF(D+→K*e+νe)/BF(D+→K-π+π+) =0.53±0.05±0.06. The non-resonant Kπ component in the D+→Kπeν decay mode was found to be small. Combining our results with measurements with the D0 lifetime and a branching fraction for the mode D0→K-π+ we find ‖Vcs‖2≡f+(0)‖2=0.50±0.07±0.08. We have observed signals for decays D+s and D+→π-π+π+. We have analysed these modes for the fraction due to ρ0π+ and f0(975)π+ and measured their relative branching fractions. Also, we present limits on flavour-changing neutral current decays D0→e+e- and D0→μe.