The Sudbury Neutrino Observatory has demonstrated that the apparent deficit in solar neutrinos observed on Earth is due to matter-enhanced flavor transitions, and provided precision measurements of the relevant oscillation parameters. The low backgrounds and large, spectral charged-current $\nu_e-d$ cross section that enabled these measurements also give SNO unique sensitivity to two yet-unobserved neutrino signals of great interest: the $hep$ solar neutrino flux and the diffuse supernova neutrino background (DSNB). This work presents a joint analysis of all three running configurations of the SNO experiment in order to improve constraints on the $hep$ and DSNB $\nu_e$ fluxes. The crucial uncertainties in the energy response and atmospheric neutrino background, as well as the event selection criteria, are reevaluated. Two analysis approaches are taken, a single-bin counting analysis ($hep$ and DSNB) and multidimensional signal extraction fit ($hep$), using a random sample representing 1/3 of the total SNO data. These searches are the most sensitive to date for these important signals, and will improve further when the full dataset is analyzed. The SNO+ liquid scintillator experiment is a successor to SNO primarily concerned with a search for neutrinoless double-beta decay ($0\nu\beta\beta$) in $^{130}$Te. The modifications to the SNO detector in preparation for SNO+ and an analysis of the $0\nu\beta\beta$ sensitivity of this upcoming experiment will also be presented in this work. SNO+ will be the first experiment to load Te into liquid scintillator, and is expected to achieve world-class sensitivity in an initial phase commencing in 2017, with significantly improved sensitivity in an upgraded configuration to follow using much higher Te target mass.