I believe it takes ordinary 10-40 oil. Harley-Davidson runs straight SAE-50 in my bike, which I found out is Chevron Delo -- rated API-SE. Delo is tough enough and long lasting enough for use in diesel engines, so it may be best to use Delo.
However, there is a lot good to say about Amsoil and Mobil 1: both are pure synthetic. The problem is that some older Kawasakis use a wet clutch, and the pure synthetic oil is too slippery for the clutch to operate.
Basically, just stick with the manufacturer recommendation.