Well, through actual STAB moves that do damage, Pokemon who don't have a very broad movepool (like Magikarp, Ditto, Caterpie, Weedle etc.) don't normally have actual STAB moves.
However, if you mean actual moves of their typing, and not STAB, after some brief research the only Pokemon I can think of is Magikarp, Feebas, Metapod, Kakuna, Silcoon and Cascoon. Understandably, I didn't want to do a heap of research, but some brief research of 'Pokemon that don't possess broad movepools' and that's all I got.
I hope I helped. :)