Sure, you can find woodworking joints more beautiful than the half-lap. And, one or two joints might be stronger. But few woodworking joints match the half-lap for all-around usefulness and ease of construction.
Before you make this cut
As you can see by the illustration, a half-lap joint consists of two workpieces reduced to half of their thickness where they lap over each other. This provides a face-grain-to-face-grain joint with plenty of gluing surface. Simple butt joints, on the other hand, rely on an end-grain-to-edge-grain bond that can break easily. Even a dowel-reinforced butt joint won't prove as strong as a half-lap.
Half-lap joints do reveal end grain on both sides of the joint, so avoid using the joint where such an appearance proves objectionable. We often use half-laps for shop-cabinet door frames, workbench leg frames, outdoor furniture, and internal web frames for furniture such as dressers.
You need only a tablesaw or radial-arm saw to make a half-lap. We prefer to use a dado set for fast and smooth results.
If you don't own a dado set that will cleanly shear cross grain and leave the sawn surface smooth and flat, we suggest you use a router table outfitted with a straight bit. Here, we show how to make corner- and T-joints with a tablesaw, but you easily can adapt these techniques to your radial-arm saw or router table.