Mount & Blade: Warband

The fastest way that I could figure out for this was to join a deathmatch or team deathmatch game on a horse-friendly map such as the arena or field by the river (of course, you need to be lucky enough for there to be a populated DM or TDM server), select the infantry class of whichever faction you want, and equip the best available spear that can be used with a shield.

Find an enemy melee cavalry player and try to get his attention. Once he's charging towards you, switch to first person mode (by pressing the left thumbstick) as this makes it much easier to aim with a spear. Hold right trigger to charge your attack (so you can see the point of your spear in 1st person mode so you can aim your strike) and keep walking towards him as he charges at you. When he's in range, jump towards him with the A button and let go of the right trigger, trying to aim the point of your spear in his chest or face (you will likely need to aim ahead just a little as the rider is a moving target).

The reason you're jumping towards him as you stab is so you get a clean full-damage shot at the rider and you don't risk accidentally hitting the horse instead. It also throws off the rider's aim with their own attack so makes it less likely that he'll kill you as you're trying to stab him.

If this is done correctly, this move will often kill them in one hit as the game's weapon damage mechanics will account for the relative momentum between the two of you (assuming the horseman is coming towards you at full speed).

With practice, I could get 4-8 kills with this method each match, assuming there were at least 2 or 3 enemy horsemen and I ignored every enemy on foot.