Stonecrop succulents like Sedum cauticola (stonecrop) and Sedum spectabile (showy stonecrop) have thick, greenish stems and leaves, and produce purple, bright pink or red flowers. The 'Brilliant' cultivar of Sedum spectabile has bright pink flowers with dark pink anthers.
Species in the Escobaria genus, native to North America from central Canada south to Mexico, produce large flowers, relative to the size of the cactus. Escobaria vivipara, also called spinystar, ball and viviparous foxtail cactus, produces bright pink, purple or yellow blooms.
Despite the name, this "cactus" is really a Brazilian succulent. Christmas cactuses (Schlumbergera bridgesii) produce flowers in orange, purple, red, cream or bright fuchsia pink. Many bloom at Christmas, but related species may bloom closer to Thanksgiving or Easter.