I recently did a little snooping around the Moby Games database and was surprised to discover that there really aren't any video games that embrace the theme of ancient naval battles. Oar driven war galleys bent on ramming, boarding or bombarding each other doesn't appear to have been a central mechanic outside of titles like the Rise and Fall: Civilizations at War series. There are a few board games that have been published over the years, but until Total War: Rome II nobody has bothered to tackle this particular slice of military history for quite awhile. I find this a bit odd considering it was the primary form of naval warfare for well over a millennium and featured a considerable number of decisive engagements between a variety of different factions. Romans, Greeks, Egyptians, Persians, Carthaginians and even peoples beyond the Mediterranean (such as Vikings and Maori) employed war galleys.
Experienced rowers were valued for their strength and endurance, as well as being able to keep tempo for hours on end. Generally speaking, war galleys only had about 30 inches of wiggle room between each oar so it was vital to maintain the rhythm of each stroke. One advantage of having two or even three rowers per oar was the fact that more senior center most oarsmen could keep their less experienced juniors in sync.
Bigger wasn't always better though. At the Battle of Actium smaller more maneuverable Roman war galleys were able to swarm larger Egyptian ships. Boarding actions were where Rome excelled. Grappling hooks, either thrown by hand or via a launcher called the "harpax", were the primary method getting up against, and on board, an enemy ship. However, the Romans also used a device called a "corvus" (Latin for "crow") to play to their strengths. Basically it was a spiked boarding ramp held vertical near the prow until it could be brought down on the deck of an opposing vessel. While effect in several major naval engagements, it had the disadvantage of making Roman war galleys top heavy and easier to capsize.
Rather than getting up close and personal another viable tactic was to bombard from a distance. Arrows and javelins worked well for this and sometimes were sent not from the ship's deck, but rather from light weight collapsible towers in order to get a height advantage over opposing vessels. Incendiary weapons were used as well, though they usually took the form of flaming projectiles or pots of oil suspended on long poles.
So, with all this said what eventually brought an end to the era of war galleys. In a word - economics. Having large teams of hard working oarsmen meant also having to keep them well nourished and hydrated. This, of course, greatly limited the maximum range a galley could travel before it need to resupply. Hence, logistics were an especially big and ever present concern for navel commanders of that era. Most galleys never left sight of land even when navigation techniques improved to the point that it was no longer necessary to hug the coastline. The reason for this was the danger of sudden storms, not to mention the need for dry land so the crew could have a place to stretch out and sleep on at night. In other words the age of war galleys came to an end when the drum beat changed from "catch and drive" to "quick and cheap."