There are a number of popular filaments that can be bought with carbon fiber fill including PLA, PET-G, Nylon, ABS, and Polycarbonate. These fibers being extremely strong, they cause the filament to increase in strength and stiffness, and also reduce its overall weight.
The carbon fibers in these filaments can be extremely abrasive. In many cases, the carbon fibers are actually harder than the brass nozzles used on most 3D printers, so trying to print these materials with a stock nozzle could damage the printer. Instead, plan on upgrading to a hardened steel hotend. These hotends can resist the added wear from the fibers, however, they also tend to be less thermally conductive than their brass counterparts. You may need to set the extruder temperature as much as 40° hotter than usual, which also helps with reducing the chance of a clog. Reducing the fan speed can also be useful to prevent thermal issues with the steel nozzles.