Superconducting properties of bulk, dense, pure MgB2 and doped (Mg(1-x)A(x))B-2 samples with A = Na, Ca, Cu. Ag, Zn and Al were studied for compositional ranges 0 < x less than or equal to 0.20. The effects on pinning properties and critical current were investigated, particularly for A = aluminium. The samples were sintered and/or synthesized at high pressure-high temperature in a cubic multi-anvil press (typically 3.5-6 GPa, 900-1000 degreesC). They were characterized by x-ray diffraction, scanning electron microscopy and their superconducting properties were investigated by ac susceptibility, magnetization (VSM and SQUID) and transport measurements under a magnetic field. Only Al really substitutes on the Mg site. The other elements form secondary phases with B or Mg which do not act as pinning centres. No positive effect is observed on the superconducting properties of the bulk MgB2 samples with these doping elements added: T-c, critical current j(c), H-irr and H-c2. For Al, the effect on H-c2 remains small. and the irreversibility line does not move, thus not improving the critical current of the Al-doped MgB2 samples.