Support elements for footwear or other products include: (a) a base member having first and second major surfaces; and (b) an extending arm having a free end for engaging a portion of a footwear structure. The extending arm may engage and further support a heel-supporting portion or other structural portion of an article of footwear or other foot-receiving device. Such foot-receiving devices may include: (a) a foot-covering member (such as a footwear upper); (b) a foot-supporting member (such as a footwear sole structure) engaged with the foot-covering member; and (c) a lateral-reinforcing member that includes an extending arm engaged with at least one of the foot-covering member or the foot-supporting member.