I have the following mesh. As you can see there are quite a bit of triangles that are unnecessary, and can be reduced. However, if I use the decimate modifier, other triangles are also decimated and morphs the shape. enter image description here

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    $\begingroup$ The decimate modifier has a lot of options. Play with the settings for planar, using Angle Limit and All boundaries for more info read: blender.org/manual/modeling/modifiers/generate/… $\endgroup$ – user1853 May 19 '16 at 17:22

If decimate is too destructive, then while in edit mode, select all, then press X>limited dissolve to remove excess edges in your model. You can adjust the angle threshold in the operator panel as needed. Don't forget to also remove doubles with W>remove doubles.

enter image description here

You can also try tris to quads. Press Spaebar and type in tris to quads, and select the operation from the menu, or or press Alt + J


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