For lukep:

In face select mode, select faces by triangle/quad/other.
Available through header menu, toolbox, or hot keys.

Hot keys are:

ctrl-shift-alt-3: Select all triangles
ctrl-shift-alt-4: Select all quads
ctrl-shift-alt-5: Select all non-triangles/quads
(maybe a bit sore for the wrist)

And also available through the menu/toolbox.

I've never used f-gons so I don't know if the 'select other'
function works there (or works at all, for that matter).

source/blender/src/toolbox.c

@@ -1645,6 +1645,9 @@ static TBitem tb_mesh_select[]= {
 {	0, "SEPR",                          0, NULL},
 {	0, "Random...",			            5, NULL},
 {	0, "Non-Manifold|Shift Ctrl Alt M", 9, NULL},
+{	0, "Triangles|Shift Ctrl Alt 3",    11, NULL},
+{	0, "Quads|Shift Ctrl Alt 4",        12, NULL},
+{	0, "Non-Triangles/Quads|Shift Ctrl Alt 5", 13, NULL},
 {	0, "SEPR",                          0, NULL},
 {	0, "More|Ctrl NumPad +",            7, NULL},
 {	0, "Less|Ctrl NumPad -",            8, NULL},