In ancient times, why do many empires strongly like to invade and conquer other countries?

Profit and exploitation.

Money.

It is in the nature of Empires to invade & conquer other countries. It is how Empires are named- for this property. If they don't do that they wouldn't be called Empires. Any other reason is an excuse or a ruse to do so.

Many different reasons. Among them are power and resources - but notoriety, fame, and the belief in the afterlife also played important roles. The practical reasons were of course the acquisition of territory and thus expansion of the tax base, acquisition of resources such as precious metals and wood, and war booty like slaves and treasures.

Alexander seemed to be driven mostly by a desire to be a renowned and feared conqueror, and to have his name echo throughout history as such - a desire that he largely fulfilled. Roman generals desired fame and prestige through the Senate's granting of Triumphs, grand ceremonies that were used to celebrate successful campaigns. Viking warriors fought and conquered with the belief that they would be destined for Valhalla in the afterlife. Another rationale is that generals and other leaders just wanted to give their soldiers something to do. Soldiers themselves were driven by greed and relied upon war spoils in many cases for their payment. If they weren't being turned loose on enemies of the State, then they might very well be turned on the State itself - as was the case on countless occasions in ancient Rome.

In the words of a semi-famous cartoon character, "Money and power; power and money." Religion has frequently been used as an excuse, but it always boils down to wanting someone else's resources or wanting to rule them, or both.

Nothing's changed - it still happens. Y's reason is correct - either religion or resources.

Same reason that they are doing it today, either religion or resources.