Probably the most famous ancient games are the gladiator battles of the Roman Empire, particularly those that took place in the well-named Colosseum [strangely, the spellchecker wants this to be Coliseum]. I think that the fights to the death between men (and occasionally women) who were typically slaves are confined to Rome. Before Byzantium arose as the second empire one chap or other forbade them altogether.
Obviously there’s lots of drama and excitement to be had when it comes to gladiators. That’s partly why the film Gladiator was such a success and why the more recent Spartacus series has been so well-received (possibly aided by the large number of naked ladies). The downside is that it’s so associated with the Roman Empire, and is not especially original. On the plus side, a gladiator battle is rather more exciting than a game of chess.
Chariot-racing is another old Roman favourite. The Circus Maximus could hold a surprisingly large 150,000 spectators, roughly twice the capacity of a modern, large football stadium. A sort of Formula Horse for the Ancient World, they were pretty rough affairs with the charioteers often trying to force their rivals into the spina (the median in the track’s centre). Intriguingly, there were four teams in Rome (Red, White, Green and Blue, eventually amalgamating into just Green and Blue) which were fanatically loyal and, in the reign of the Byzantine Emperor Justinian had what almost amounted to a civil war that threatened the emperor himself. Whilst not overtly deadly, chariot-racing could easily lead to fatalities, and the fans were perhaps just as dangerous as the races.
Tabula is, apparently, an ancestor of backgammon (I was just checking it on Wikipedia) and an enjoyable game. Unlike gladiatorial combat and chariot-racing, I have actually played it, and it does require some thinking although there’s a hefty element of luck involved as well. It’s a board game where players move their pieces around in progress from square I to XXIV. Enemy pieces can be captured by landing on that square (provided the enemy piece is alone), and pieces can only successfully leave the board once all remaining pieces are on the board. The rules indicated on Wikipedia are moderately different to the ones I played by (I used two dice rather than three), but it’s basically the same. It’s a surprisingly tactical game and it’s possible to be unable to move (if you have a single piece on square XX and the enemy has three pieces each on XXI and XXIII and XXIV and you roll a I and a III there’s no square you can land on). Pretty lengthy, two player only and a bit tactical. Lacks the probably of impending doom that the previous games have, but it is better for scheming confederates to play whilst plotting woe and terror. I think Nero had one fixed to his chariot.
There’s quite a nice dice game called Mexicana, but an ancient (approximate) equivalent is Meier, a Viking game. Meier involves throwing two dice, with certain scores being better than others. However, you are allowed to deceive the other players and claim a better score, as every sequential score must be better than the last *or* the player who throws poorly must throw more money into the pot. As all you need is two dice and a mug, or something else to cover the dice, it’s a game the meanest peasant could play.
King’s Table, or the rather ugly-sounding Hnefatafl, is a kind of Viking chess. Unlike chess, however, the two sides are not even. Only one has a King, and that player starts with his pieces in the centre and aims to have the King escape the board. The other player has four clusters of pieces, a cluster per edge, and seeks to capture the King. Of course, chess is another option, but sometimes using even legitimately ancient things in fantasy stories can seem out of place if they’re still in modern use.
I got my info about Meier and Hnefatafl from this site, where you can buy related stuff (NB I haven’t actually bought any and I’m not affiliated to the website in any way):
There’s a lot of political discord in Spain right now regarding bullfights, but until quite recently the British were also lovers of blood sports. Cockfights were tremendously popular, and as chickens are not the priciest of animals (tedious fact: chicken is the most efficient meat in terms of land usage, as well as being handy due to the eggs) even small villages could have a cockpit. Obviously this would have to be a communal game.
Last but not least: bareknuckle boxing. Somewhat oddly, this is safer than, er, gloved boxing. The fact is that boxing gloves are bloody good at protecting your own hands but don’t cushion the blows that strike your foe. Human knuckles are only so tough, and smashing them into a jawbone is a good way to bruise or break them. A nice, relatively safe form of fighting (certainly compared to gladiatorial combat) which could take place almost anywhere.