We report the first observation of a b-->u type charmless baryonic B decay, B+-->pppi(+), as well as b-->s type B0-->ppK0 and B+-->ppK(*+) decays. The analysis is based on a 78 fb(-1) data sample recorded on the Upsilon(4S) resonance with the Belle detector at KEKB. We find B(B+-->pppi(+))=(3.06(+0.73)(-0.62)+/-0.37)x10(-6), B(B0-->ppK0)=(1.88(+0.77)(-0.60)+/-0.23)x10(-6), and B(B+-->ppK(*+))=(10.3(+3.6+1.3)(-2.8-1.7))x10(-6). We also update B(B+-->ppK+)=(5.66(+0.67)(-0.57)+/-0.62)x10(-6) and present an upper limit on B(B0-->ppK(*0)) at the 90% confidence level. A common feature of the observed decay modes is threshold peaking in baryon pair invariant mass.