Ultra-broadband THz photonics covering the 0.3-20 THz range provides a very attractive foundation for a wide range of basic research and industrial applications. However, the lack of ultra-broadband THz devices has yet to be overcome. In this work, high-density organic electro-optic crystals are newly developed for efficient THz wave generation in a very broad THz spectral range and are successfully used for a broadband THz time-domain spectroscopy. The new organic THz generator crystals, namely the OHP-TFS crystals, have very low void volume, high density, and are shown to cover the ultra-broadband THz spectrum up to about 15 THz, which cannot be easily accessed with the more widely used inorganic-based THz generators. In addition to the very favorable broadband properties, the generated THz electric-field amplitude at the pump wavelength of 1560 nm is about 40 times higher than that generated by a commercial inorganic THz generator (ZnTe crystal). By using the newly developed OHP-TFS as generation crystal in a compact table-top all-organic THz time-domain spectrometer based on a low-cost telecom fiber laser, the optical characteristics of a model material are successfully determined in the broad 1.5-12.5 THz range with high accuracy.