Rubik's Cube
The classic 3x3 cube made by Rubik's Cube is available through many stores, as well as the company website. In addition to the 3x3, it makes a Mini Cube (which is a 2x2), a 4x4 cube and a 5x5 cube. There is also a Touch Cube, which uses touch sensors so that, instead of moving parts, one can swipe the the puzzle pieces around to solve it. Rubik's also sells kits for constructing a Rubik's Cube at home, for those who want to tweak the cube for speed.
Verdes Innovations
Verdes Innovations is a European company that makes puzzle cubes like the Rubik's Cube. While it does not sell any of the typical 3x3 cubes that are so iconic, Verdes Innovations does sell much larger cubes than Rubik's makes. They are called V-Cubes, and V-Cubes are available in 2x2, 4x4, 5x5, 6x6 and 7x7. Verdes Innovations also offers V-Cubes in a variety of color combinations, designed to match the flags of many European countries, including Denmark, France, Sweden, Spain and more.
Maru
Maru is a brand that focuses on making cubes for speed-cubing (solving the puzzle as fast as possible). It also offers a variety of colors in the 3x3 formation, including a transparent cube, cubes with different base colors under the stickers (such as green and yellow). Maru offers sticker kits for cubes as well. Some are for replacing old stickers, and some are for personalizing the cubes with music notes or domino dots.
Haiyan's Cube
Haiyan Zhuang is notable for having solved the 3x3 cube, blindfolded, in 30.94 seconds. He holds a record for it, having the second fastest blindfolded cube solving time ever. This led him to design a cube specifically for speed solving while blindfolded, which is available in two base colors: black and white.