I'm currently playing a game on Emperor, playing the Chinese (thus no knights from me). I have taken my continent (huge one), only one Arabic city (flipped after we peaced) remains. India has an island with a city, Arabia has an island with two. Don't see much point in taking them, so I'll let them be. Now, I know what you're thinking. Arabia, India and China don't have knights. Neither do Mongols or Japan that also were civs. And I did cripple Korea first. And, admittedly, I did see one elephant. If you're not interested in hearing the game story, skip the below part of the post and just read my next post.
I started on a square with three(!) cows and a river. Not a shabby start. I got a settler in my first hut. Ok, so it's a great start. I start expanding while building an archer army, looking at some tasty Japanese just north of me (I was in SE corner). Then, Arabia to my east declares, so I direct my archers that way. After a few razed cities I get some nice techs in exchange for peace. Immediatly after Korea (to my NW) declares. Same thing there, raze a few cities then got techs for peace. This cleared up a lot of space for me to expand, and gave me three luxuries I wouldn't have gotten otherwise. No Great Leader though
After that I reverted to my old builder style for a while, trying to hurry to Riders. Right as I enter the middle ages Korea declares again and snatches a city. Oh well, time to train some horsies that can be upgraded. After a slow start of the war (only built horsies in cities with libs and marketplaces already built), it didn't take long after my riders came to wipe the eastern part of Korea, leaving them with a few cities west of Arabia. Especially since I quickly got two GL that gave me a FP and Sun Tzu (my first wonder!).
Next, I turned my attention to the Japanese. When you build the Pyramids in a city bordering my civilization you're begging for it. Japan, just like Korea had spearmen as their defenders. Like that's a challenge for my riders. They had a lot of jungle in their territory though, which slowed me down.
Arabia decided to go to war with me again. Great plan. They actually had one Pikeman in their empire. And several Medieval Infantry units. They were small though, after my early war with them, so it didn't take long.
North of former Japan were India (to the west) and Mongolia (to the east). Mongolia decided to declare on me (they did get a free city for it). The turn after I get Cav. Upgrade, then head north. I still had a few turns left before the peace treaty with Korea expired anyway. During the time it took me to get a big enough army north to Mongols the peace treaty expired with Korea and I decided to kill them both. These guys had pikemen, which evened out since I had Cav now. Korea went quickly, Mongols took a little time due to distance.
Halfway through Mongols I decide to kill the Indians as well. By now I had former Japan, former Arabia and former Korea producing Cav as well so it wasn't a problem. That's when I saw it. An elephant! A regular Elephant. Oh well, he was in the way so I killed him. Sorry. After killing the last Indian city on the continent I peaced them. Mongolia fell the same turn. Reasearched democracy and I'm now aiming for a cultural victory.