The Antonov AN-124 is a Russian (and Ukrainian) -built aircraft with a greater cargo capacity (330,000 lb / 150,000 kg) than the comparable US-built airplanes. Takeoff weight 893,000 lb (405,000 kg). These behemoths have been used to transport whales and elephants, along with more mundane cargo such as jet engines (for the B777 and A380), rockets and satellites, and pieces of airliners (for Boeing and Airbus). One operational quirk is that the airplane has to sit in takeoff position on the runway for several minutes before it can begin rolling for takeoff. So far I've been unable to get a coherent explanation from anyone on why this is so.
The Lockheed C-5 Galaxy has a maximum takeoff weight of 840,000 lb (381,000 kg). Unlike the AN-124, which has civilian operators, the C-5 is only flown by the US military. Payload capacity is 270,000 lb (122,470 kg).
The C-17 Globemaster III is built at the former McDonnell-Douglas (now Boeing) plant in Long Beach, California; I get to see them fly over the house when they depart. With a takeoff weight of 585,000 lb (265,350 kg) and payload of 170,900 lb (77,519 kg), the C-17 is a good bit smaller than the C-5. Besides the US military, C-17s are also flown by the forces of Australia, Canada, Great Britain, NATO, Qatar, and the United Arab Emirates. Boeing offered a commercial version for a while, but there were no buyers.