Inkscape - rounding corners of shapes?

since Inkscape 1.0 + we have LPE Corners (changer/fillet)

1. Select object
2. Go to Path/ Path effects
3. Add Corners (Fillet/Chamfer) by clicking on +
4. Adjust the size of corners with the node tool by dragging green nodes or in the dialog

GIF how to add custom round corners

1. Select the rectangle or square
2. Select the nodes option
3. On the right hand corner, you will see a round node instead of a square node. Drag down the node until you get the rounded corner you want.

The nodes option:

Round widget you need to drag to get rounded corners:

What happens when you drag the round widget:

As others have noted this only works on rectangles (but that is a common use case that will land people on this page).