Axes Origin & Labels in 3D Plot

With Scaled position:

Show[{Plot3D[x^2 + y^2 + 3, {x, -3, 3}, {y, -3, 3}, 
      AxesOrigin -> {0, 0, 0}, PlotRange -> {-1, 20}], 
  Graphics3D[{Text["x", Scaled[{-.05, .5, 0}], {0, -1}], 
    Text["y", Scaled[{.5, -.05, 0}], {0, -1}], 
    Text["z", Scaled[{.5, .5, 1.1}]]}]}, Boxed -> False]

You can add them manually:

Show[{Plot3D[x^2 + y^2 + 3, {x, -3, 3}, {y, -3, 3}, 
 AxesOrigin -> {0, 0, 0}, PlotRange-> {-1, 20}], 
 Graphics3D[{Text["x", {3, 0, 0}], Text["y", {0, 3, 0}], Text["z", {0, 0, 20}]}]}]

Mess around with the Text[ ] functions to change sizes and positions. I'm sure there must be a better way, though.