Impact-attenuating elements, e.g., for use in footwear or other foot-receiving device products, may include: (a) a base member, such as a fluid-tight and/or other fluid-filled or fluid-containing enclosure element; (b) a support element integrally and contiguously formed in a surface of the base member; and/or (c) a spring device engaged with the support element. The support element and its corresponding spring device (if any) may include a non-planar surface (e.g., substantially parabolic shaped, cylindrically shaped, etc.) that extends in a direction into the base member and toward its opposite surface. The support element and its corresponding spring device (if any) also may include reinforcing structure(s), such as raised ribs extending along a surface of the support element and/or spring device.