I concur with the previous comment about berserkers, an amphibious unit that requires no resources to build.
I'd also add the Sumerian enkidu warrior. Yes, it looks and acts like a spearman, but it's not just a spearman- it's a 1/2 price spearman! Recently the enkidu warriors saved me big time. I was playing emperor level on a standard size random map that turned out to be small land mass with normal distribution.
I kid you not, I got jumped in the first ten turns of the game. Before I had my first capital culture expansion, four enemy warriors were at the gates, with only one enkidu warrior garrisoning the capital. This one warrior defeated all four, becoming elite in the process. In the ensuing conflict, enkidus proved very adept at garrisoning cities and defending offensive units, especially since they only cost 10 gold to build. This cheap production cost enabled me not only to drive the enemy into the sea, but to expand cheaply as well.