We discuss several types of integrated photonic LiNbO3 waveguides supporting propagation of modes which can be classified as bound states in the continuum (BICs). The key properties leading to the existence of BICs (or quasi-BICs) considered here are the material anisotropy, the waveguide birefringence, or the combination of both. Typical examples are titanium diffused and proton exchanged waveguides in bulk LiNbO3 crystals and recently proposed dielectric-loaded waveguides on LiNbO3 thin films. Proton exchanged waveguides in thin film LiNbO3 are considered, too. These waveguide structures are discussed from the point of view of their benefit for applications, especially in electro-optic devices.