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/include/BIF_editmesh.h

@@ -127,6 +127,7 @@ extern void editmesh_align_view_to_selected(struct View3D *v3d, int axis);
 
 	/* Selection */
 extern void select_non_manifold(void);
+extern void select_faces_by_numverts(int numverts);
 extern void select_more(void);
 extern void select_less(void);
 extern void selectrandom_mesh(void);

source/blender/src/editmesh_mods.c

@@ -1395,6 +1395,44 @@ void reveal_mesh(void)
 	BIF_undo_push("Reveal");
 }
 
+void select_faces_by_numverts(int numverts)
+{
+	EditMesh *em = G.editMesh;
+	EditFace *efa;
+
+	/* Selects isolated verts, and edges that do not have 2 neighboring
+	 * faces
+	 */
+	
+	if(G.scene->selectmode!=SCE_SELECT_FACE) {
+		error("Only works in face selection mode");
+		return;
+	}
+
+	efa= em->faces.first;
+	while(efa) {
+		if (efa->e4) {
+			EM_select_face(efa, (numverts==4) );
+		}
+		else if (efa->e3) {
+			EM_select_face(efa, (numverts==3) );
+		}
+		else 
+			EM_select_face(efa, (numverts!=3) && (numverts!=4) );
+		efa= efa->next;
+	}
+
+	countall();
+	addqueue(curarea->win,  REDRAW, 0);
+
+	if (numverts==3)
+		BIF_undo_push("Select Triangles");
+	else if (numverts==4)
+		BIF_undo_push("Select Quads");
+	else
+		BIF_undo_push("Select non-Triangles/Quads");
+}
+
 void select_non_manifold(void)
 {
 	EditMesh *em = G.editMesh;

source/blender/src/header_view3d.c

@@ -828,6 +828,16 @@ void do_view3d_select_meshmenu(void *arg, int event)
 		case 9: /* select less */
 			select_non_manifold();
 			break;
+		case 11: /* select triangles */
+			select_faces_by_numverts(3);
+			break;
+		case 12: /* select quads */
+			select_faces_by_numverts(4);
+			break;
+		case 13: /* select non-triangles/quads */
+			select_faces_by_numverts(5);
+			break;
+
 	}
 	allqueue(REDRAWVIEW3D, 0);
 }
@@ -859,6 +869,19 @@ static uiBlock *view3d_select_meshmenu(void *arg_unused)
 	uiDefBut(block, SEPR, 0, "", 0, yco-=6, 
 			 menuwidth, 6, NULL, 0.0, 0.0, 0, 0, "");
 
+	uiDefIconTextBut(block, BUTM, 1, ICON_BLANK1, 
+					 "Triangles|Ctrl Alt Shift 3", 
+					 0, yco-=20, menuwidth, 19, NULL, 0.0, 0.0, 1, 11, "");
+	uiDefIconTextBut(block, BUTM, 1, ICON_BLANK1, 
+					 "Quads|Ctrl Alt Shift 4", 
+					 0, yco-=20, menuwidth, 19, NULL, 0.0, 0.0, 1, 12, "");
+	uiDefIconTextBut(block, BUTM, 1, ICON_BLANK1, 
+					 "Non-Triangles/Quads|Ctrl Alt Shift 5", 
+					 0, yco-=20, menuwidth, 19, NULL, 0.0, 0.0, 1, 13, "");
+
+	uiDefBut(block, SEPR, 0, "", 0, yco-=6, 
+			 menuwidth, 6, NULL, 0.0, 0.0, 0, 0, "");
+
 	uiDefIconTextBut(block, BUTM, 1, ICON_BLANK1, "More|Ctrl NumPad +",
 					 0, yco-=20, menuwidth, 19, NULL, 0.0, 0.0, 1, 7, "");
 	uiDefIconTextBut(block, BUTM, 1, ICON_BLANK1, "Less|Ctrl NumPad -",

source/blender/src/space.c

@@ -1026,6 +1026,10 @@ static void winqreadview3dspace(ScrArea *sa, void *spacedata, BWinEvent *evt)
 						flip_subdivison(ob, 3);
 					}
 				}
+				else if ( G.qual == (LR_SHIFTKEY | LR_ALTKEY | LR_CTRLKEY) ) {
+					if ( (G.obedit) && (G.obedit->type==OB_MESH) )
+						select_faces_by_numverts(3);
+				}
 				else do_layer_buttons(2); 
 				break;
 				
@@ -1035,11 +1039,21 @@ static void winqreadview3dspace(ScrArea *sa, void *spacedata, BWinEvent *evt)
 						flip_subdivison(ob, 4);
 					}
 				}
+				else if ( G.qual == (LR_SHIFTKEY | LR_ALTKEY | LR_CTRLKEY) ) {
+					if ( (G.obedit) && (G.obedit->type==OB_MESH) )
+						select_faces_by_numverts(4);
+				}
 				else do_layer_buttons(3); 
 				break;
 				
 			case FIVEKEY:
-				do_layer_buttons(4); break;
+				if ( G.qual == (LR_SHIFTKEY | LR_ALTKEY | LR_CTRLKEY) ) {
+					if ( (G.obedit) && (G.obedit->type==OB_MESH) )
+						select_faces_by_numverts(5);
+				}
+				else do_layer_buttons(4);
+				break;
+
 			case SIXKEY:
 				do_layer_buttons(5); break;
 			case SEVENKEY:

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},