Fixing a large (1/8"-wide) crack in a wood exterior door panel
Though the crack is diagonal it looks relatively straight. In this case I'd take a piece of wood the approximate thickness of the crack at it's widest, cut it to length and then taper it so that it fits quite snugly - you should have to use a mallet to tap it home. Don't worry about the thickness too much - but obviously it should be fairly close.

Once this fits use wood glue to bed it in and fill the imperfections, though you might get a better finish using wood filler for this. Basically put more glue in than you need so it gets squeezed into every nook and cranny. Clean it off before it sets, then leave the repair to set.

Once set use a chisel to remove the excess from both sides of the panel and finally sand to make it flush with the panel. Fill any remaining (and hopefully small) holes, prime and paint.

By making the fit tight you minimise the chances for it to move, and therefore crack, further.