All-Purpose
Green car axle grease will work, but something made for a bicycle will work better. Park Tool Polylube 1000, Buzzy's Slick Honey All-Purpose Grease, Tri-Flow Synthetic Grease, or Rock 'N' Roll Red Devil will all work. Most loose ball-bearing systems can be lubricated with all-purpose grease, including headsets, bottom brackets, hubs and pedals.
Special Purpose
Grease can be formulated for specific parts of a bicycle. Some parts require grease with more heat resistance, others require low viscosity. Coaster brakes, multispeed hubs and some free hubs usually require special-purpose grease. Shimano makes greases specially formulated for their Nexus hub and coaster brake systems. They also make SIS SP41, which is formulated for shift cables. DT Swiss designed a grease for its free-hub ratchet.
Waterproof
Most grease has a certain level of water resistance, but grease specially formulated to keep out water takes on less contaminants and remains in place longer. Most grease formulated for bicycle bearings is waterproof, such as Phil Wood Waterproof Grease.
Ceramic
Ball bearings made from ceramics perform at their best with grease formulated for ceramics. Many ceramic-bearing manufacturers design grease specific to their bearings. Many contain ceramics themselves, such as Finish line Ceramic Grease.
Teflon
Teflon is used to increase durability. This type of grease can handle more revolutions than typical grease. DuPont Teflon Bearing Grease is an example.
Biodegradable
Synthetic, non-toxic, biodegradable grease can be used on bicycle bearings. These include Pedros Bio-Grease and White Lightning Crystal.