3D scatter plot with crosses

Just to illustrate:

Manipulate[
 Graphics3D[Text[marker, #] & /@ data],
 {marker, {"+", "x", Style["+", Red], Style["+", Bold]}}, 
 Initialization :> (data = RandomReal[1, {100, 3}])]

Alternatively to ubpdqn's suggestion, and in order to preserve the styling and default options of ListPointPlot3D I propose this solution:

ListPointPlot3D[RandomReal[10, {20, 3}]] /. Point -> Map[Text["+", #] &]

The trick is in this replacement rule:

/. Point -> Map[Text["+", #] &]

InputForm[ChemicalData["Methane", "MoleculePlot"]]

moleculePlot[poiints_] := Show[Graphics3D[
 {
  Translate[ 
     GraphicsComplex[
       {
        {0.0115361, -0.00644059, -0.0023318}, 
        {-6.98724, 109.314, 19.6968}, 
        {-53.4044, -24.1997, -94.6041}, 
        {-46.6211, -55.8814, 84.2109}, 
        {107.001, -29.2263, -9.30131}, 
        {-3.48785195, 54.653779705, 9.8472341},
        {-26.69643195, -12.103070295, -47.303215900000005}, 
        {-23.30478195, -27.943920295, 42.104284099999994}, 
        {53.50626805, -14.616370295, -4.651820900000001}}, 
       {
        {RGBColor[0.65, 0.7, 0.7], 
           Sphere[2, 24.],
           Sphere[3, 24.], 
           Sphere[4, 24.], 
           Sphere[5, 24.]
        }, 
         {RGBColor[0.4, 0.4, 0.4], 
           Sphere[1, 34.]}, 

         {RGBColor[0.65, 0.7, 0.7], 
           Cylinder[{6, 2}, 15.], 
           Cylinder[{7, 3}, 15.], 
           Cylinder[{8, 4}, 15.], 
           Cylinder[{9, 5}, 15.]}, 
         {RGBColor[0.4, 0.4, 0.4], 
           Cylinder[{1, 6}, 15.], 
           Cylinder[{1, 7}, 15.], 
           Cylinder[{1, 8}, 15.], 
           Cylinder[{1, 9}, 15.]}}], #]
       }
   ] & /@ (500*poiints)]

>

 somePoints = {{1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}, {1, 1, 
5}, {1, 2, 1}, {1, 2, 2}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 
1}, {1, 3, 2}, {1, 3, 3}, {1, 3, 4}, {1, 3, 5}, {1, 4, 1}, {1, 4, 
2}, {1, 4, 3}, {1, 4, 4}, {1, 4, 5}, {1, 5, 1}, {1, 5, 2}, {1, 5, 
3}, {1, 5, 4}, {1, 5, 5}, {2, 1, 1}, {2, 1, 2}, {2, 1, 3}, {2, 1, 
4}, {2, 1, 5}, {2, 2, 1}, {2, 2, 2}, {2, 2, 3}, {2, 2, 4}, {2, 2, 
5}, {2, 3, 1}, {2, 3, 2}, {2, 3, 3}, {2, 3, 4}, {2, 3, 5}, {2, 4, 
1}, {2, 4, 2}, {2, 4, 3}, {2, 4, 4}, {2, 4, 5}, {2, 5, 1}, {2, 5, 
2}, {2, 5, 3}, {2, 5, 4}, {2, 5, 5}, {3, 1, 1}, {3, 1, 2}, {3, 1, 
3}, {3, 1, 4}, {3, 1, 5}, {3, 2, 1}, {3, 2, 2}, {3, 2, 3}, {3, 2, 
4}, {3, 2, 5}, {3, 3, 1}, {3, 3, 2}, {3, 3, 3}, {3, 3, 4}, {3, 3, 
5}, {3, 4, 1}, {3, 4, 2}, {3, 4, 3}, {3, 4, 4}, {3, 4, 5}, {3, 5, 
1}, {3, 5, 2}, {3, 5, 3}, {3, 5, 4}, {3, 5, 5}, {4, 1, 1}, {4, 1, 
2}, {4, 1, 3}, {4, 1, 4}, {4, 1, 5}, {4, 2, 1}, {4, 2, 2}, {4, 2, 
3}, {4, 2, 4}, {4, 2, 5}, {4, 3, 1}, {4, 3, 2}, {4, 3, 3}, {4, 3, 
4}, {4, 3, 5}, {4, 4, 1}, {4, 4, 2}, {4, 4, 3}, {4, 4, 4}, {4, 4, 
5}, {4, 5, 1}, {4, 5, 2}, {4, 5, 3}, {4, 5, 4}, {4, 5, 5}, {5, 1, 
1}, {5, 1, 2}, {5, 1, 3}, {5, 1, 4}, {5, 1, 5}, {5, 2, 1}, {5, 2, 
2}, {5, 2, 3}, {5, 2, 4}, {5, 2, 5}, {5, 3, 1}, {5, 3, 2}, {5, 3, 
3}, {5, 3, 4}, {5, 3, 5}, {5, 4, 1}, {5, 4, 2}, {5, 4, 3}, {5, 4, 
4}, {5, 4, 5}, {5, 5, 1}, {5, 5, 2}, {5, 5, 3}, {5, 5, 4}, {5, 5, 
5}};

>

moleculePlot[somePoints]