Warmongering is more than just a diplomatic consequence; it can be a state of mind, considered a most honorable thing from a certain point of view. It is believed that a soldier in Napoleon's early days of conquest saw his General and Emperor’s constant warmongering to be of righteous cause! There are, however, some stiff penalties for launching a non-justified, or lack of Casus Belli, war.
A player who launches into a non-Casus Belli war (see the section on Casus Belli under Diplomacy) will start to accumulate diplomatic warmongering penalties from other civilizations that player has come in contact with, on top of any war weariness already suffered. Launching a surprise war, capturing opposing civilizations cities, razing captured cities, and using nuclear devices increases the diplomatic penalty based on what era the player is in.
The other approach is to denounce the opposing civilization first and then declare war formally. With this avenue to war, the warmonger penalties are NOT increased and there is the opportunity to use a Casus Belli to reduce those penalties. However, because you must first denounce your opponent, such a plan is "telegraphed" for the target and you will not have the advantage of surprise.