The invention relates to a self-stabilizing support assembly (14) for an item of furniture, such as a table, stool or chair. The assembly includes a support structure (16) for connection at an upper end thereof to an upper portion of an item of furniture. The support structure has a first pair of feet (50) at a lower end (22) thereof. An elongated guides pin (38) projects from a lower end of the support structure. A displaceable support member (30), which has a second pair of feet (32), is provided with a housing (36) defining a guide passage, in which guide passage the guide pin is longitudinally slidably received. The housing is constructed such that a cross-sectional area of the guide passage is adjustable, to permit dimensioning of the guide passage relative to the guide pin such that automatic frictional engagement of the guide pin with walls of the housing defining the guide passage occurs in response to pivoting of the displaceable support member about a pivot axis transverse to the housing, to anchor the displaceable support member frictionally against sliding displacement relative to the guide pin.