Sometimes you can find a wide angle prime lens that focuses unusually close; the Nikon 28mm/2.8 Ais comes to mind.
Front supplementary plus diopter lenses generally are weak with wide lenses, and tend to wipe out sharpness at the sides of the frame, even with the prime lens stopped down.
Extension tubes work with wide angle prime lenses fairly reliably, but with one caveat: the wider the lens, the thinner the extension tube is required. When you get down to 28/24/20mm, the required extension often becomes smaller than any available tube.
Zooms add an additional issue: extending a zoom throws off the calculations the designers made to keep zoom and focus controlled, and the result can be a situation where you end up using the zoom ring to set focus...crazy, eh?
As has been mentioned , the 24mm tilt shift lenses, from both Canon and Nikon(and Samyang?) focus exceptionally close.