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Yes. One time that I know of, the mongols. One must understand however that its not how it started, Genghis himself started out as a normal steppe conquerer but long run of success eventually created a ideology of world conquest. They did defeat every major civilisation in eurasia and conquered many. We also know that militarily speaking most of the rest of the earth never mattered that much, since they lacked technology.

Some people managed to evade the grasp of the mongols, notable the Mamluk Sultanate (or what eventually would be the Mamluk Sultanate). They made it thanks to a combination of strong but small military and internal mongol politics.

The states of west europe and part of central europe escaped as well. They were extremely lucky to evade attack thanks to mongol internal politics.

The most important area that escaped was the subcontinent of india. They made several small attempts to invade into the indian subcontinent but were pushed back. They never sent one of there giant expeditions there.

So I would argue we a few rulers surviving longer, or the complicated internal politics going a bit different, they could have conquered all of eurasia (this means all the 'civilisation' not of course tribal people that live in deserts and jungles).

They ended up with the second biggest empire of all time, only surpassed by the Brits. I however think there conquest was somewhat more impressive because they conquered civilisation that were better in technology, richer and had more troupes.

Alexander the Great sought to conquer the whole known world. He got as far as India/Pakistan but had to turn back when his soldiers wouldn't go any further. Even after he had returned to Babylon he had immediately begun plans for a new campaign. He contemplated the region around the Caspian Sea, the Arabian Peninsula, Carthage, and Rome which at this point was in the early stages of its republic. He opted to go for the Arabian Peninsula and began to plan the campaign but died before the campaign began. At the end his empire spanned from Greece and Egypt at the westernmost point to India at the Easternmost point.

Follow up: What about Rome?

They had a pretty big empire, although it seems they mostly expanded to either get rid of a threat or for personal political gain (i.e. Caesar in Gaul).

Was there a underlying ideology/policy to romanize as much of the world as possible, or did they grow so big by 'accident'?