1. Smilodon (specifically *Smilodon fatalis*): This is the most famous and iconic saber-toothed cat, often depicted in art and media. They were found in North and South America during the Pleistocene epoch.
2. Homotherium: This genus was widely distributed in North America, Europe, Asia, and Africa. They had longer legs than Smilodon and likely hunted in packs.
3. Machairodus: Another widespread genus, these saber-tooths lived during the Miocene and Pliocene epochs. They were larger than Smilodon but had slightly shorter sabers.
4. Megantereon: This genus inhabited Europe, Asia, and Africa during the Miocene and Pliocene epochs. They were smaller than Smilodon but had very long sabers.
5. Xenosmilus: This genus was found in North America during the late Pliocene and early Pleistocene epochs. They were very large and powerful, with shorter, thicker sabers than Smilodon.
It's important to note that these are just a few examples, and there are many other extinct saber-toothed cat species that have been discovered.