KTP will double till about 528nm, above this in the blues you need Bibo (Bismeuth B-borate), BeBO (beryllium B borate) or KNbo3 (potassium Niobate) Of these BiBo is the most efficient, but is also the most easily damaged from optical power.
If doing hard UV you need LBO (lithium B-borate) or BBO (B-Barium Borate)
Really high power stuff uses the dihydrogen phosphate and Arsenate series crystals. Ie KDP, RbDP RbH2AsO4, NH4H2Po4 etc.
The last one you can grow from superphosphate fertilizer as easily as rock candy! Get a nice crystal, polish the sides with 1800- grit sand paper, clean with naphtha, place a drop of mineral oil and a microscope cover slip on each polished side, and you can get strong green pulses with a SSY-1 Q-switched yag laser without trying very hard.
The best all around nonlinear crystal is PPLN (periodically poled Lithium Niobate) for shorter wavelengths, and periodically poled KTP for longer wavelengths to about 4.2um.
An excellent example of this is the crystals MI Lasers is selling, it is optimized for 1.5um, however you can get 755nm light out by pumping with a varo q-switched erbium laser, and if you are really creative you can even get about 500nm stoplight led blue-green light out with one of these- not easy, but doable.
The mid to far IR is covered with exotic crystals such as BiCdTe, and PbTe as well as doped sulfides of cadmium, mercury and lead.