Search results for nucleon decays p→e^{+}X, p→μ^{+}X, n→νγ (where X is an invisible, massless particle) as well as dinucleon decays np→e^{+}ν, np→μ^{+}ν, and np→τ^{+}ν in the Super-Kamiokande experiment are presented. Using single-ring data from an exposure of 273.4 kton·yr, a search for these decays yields a result consistent with no signal. Accordingly, lower limits on the partial lifetimes of τ_{p→e^{+}X}>7.9×10^{32} yr, τ_{p→μ^{+}X}>4.1×10^{32} yr, τ_{n→νγ}>5.5×10^{32} yr, τ_{np→e^{+}ν}>2.6×10^{32} yr, τ_{np→μ^{+}ν}>2.2×10^{32} yr, and τ_{np→τ^{+}ν}>2.9×10^{31} yr at a 90% confidence level are obtained. Some of these searches are novel.