Silicon nitride (Si3N4) waveguides offer low-loss wave propagation over a wide spectral range including visible wavelengths and lend themselves to photonic integrated circuits for bio-photonic applications. The Si3N4 device portfolio, however, is so far limited to passive devices that need to be fed by external light sources. This often requires delicate and costly fiber-chip coupling schemes that are subject to stringent alignment tolerances. In this paper, we present and investigate a class of lasers that combine Si3N4 waveguides with light-emitting organic cladding materials in a hybrid approach. These Si3N4-organic hybrid (SiNOH) lasers are operated by optical pumping from the top with low alignment precision. We theoretically and experimentally investigate different SiNOH laser concepts based on spiral-shaped ring resonators and distributed feedback (DFB) resonators. While our devices are designed for an emission wavelength of approximately 600 nm, the SiNOH laser concept can be transferred to a large range of wavelengths in the visible spectrum. The devices are amenable to cost-efficient mass production and have the potential to address a wide range of applications in bio-photonics and point-of-care diagnostics.