Most cactus flowers bloom from the middle of the spring to the middle of the summer. However, other varieties last for an even briefer period of time. For example, the night-blooming cactus only blooms for a few hours at night.
Christmas cacti bloom just during the winter. The Thanksgiving cactus blooms a few weeks before the Christmas cactus; you can easily identify this variety as the last part of the stem has two teeth.
Unlike other blooms, the flower on a cactus actually grows inside out. According to the University of Texas, you are not seeing any flower tissue at all except for the sepals and petals at the very tip when you look at a cactus flower; all the rest is vegetative stem and leaf, and the true flower parts are inside.
The 1969 movie "Cactus Flower" was Goldie Hawn's first film debut. The film does contain a cactus which at some point towards the end, does actually bloom.