Highly recommended NLO Crystals list from Yutai Optics:
LBO, BBO, KTP, KTA, KDP, LiNbO3, MgO: LiNbO3.
    LBO (Lithium Triborate) crystals are excellent nonlinear crystal. For frequency doubling(SHG), tripling(THG) of Nd: YAG, Nd: YLF, Nd: YVO4 lasers, it is one of the most useful nonlinear optical materials in ultraviolet and visible laser applications.

    BBO (Beta-Barium Borate)crystals are important nonlinear optical crystals with combination of unique optical properties.Broad transmission and phase matching ranges, large nonlinear coefficient, high damage threshold and excellent optical homogeneity provide attractive possibilities for various nonlinear optical applications.

    KDP and DKDP (Potassium Dihydrogen Phosphate and Potassium) are one of the most widely-used commercial NLO materials, characterized by good UV transmission, high damage threshold, and high birefringence, though their NLO coefficients are relatively low. They are usually used for doubling, tripling and quadrupling of a Nd: YAG laser under the room temperature. In addition, they are also excellent electro-optic crystals with high electro-optic coefficients, widely used as electro-optical modulators, such as Q-switches, Pockels Cells, etc.

    KTP(Potassium Titanyl Phosphate) crystals are the most widely used material for frequency doubling of Nd-doped lasers, particularly at the low or medium power density. It is widely used for frequency mixing to generate Red/Green/Blue output, and for OPO and OPA to generate visible to mid-infrared tunable output. It is also used for many E-O devices such as Q-switches and E-O modulators.

    Potassium Titanyl Arsenate(KTiOAsO4), or KTA crystals, are excellent nonlinear optical crystal for Optical Parametric Oscillation (OPO) application. It has better non-linear optical and electro-optical coefficients, significantly reduced absorption in the 2.0-5.0 μm region, broad angular and temperature bandwidth, low dielectric constants. And its low ionic conductivity result in higher damage threshold compared with KTP.