Perhaps you mean fundamental operations instead of operations. Others have noted that composition, projection, and changing one's point of view allows you to handle operations of higher arity.
I imagine that fundamental operations are usually of such low arity because we prefer simplicity. Doing the maximum or the sum of a tuple of numbers can be acheived by iterating the corresponding binary operation on certain parts of the tuple. Anything more gets uncomfortably complicated.
Having said that, there are examples like multi-linear functions (especially the determinant) that come up in various fields of analysis, not to mention infinitary operations like integration. Even then, we like to break things down into iterates of simpler terms, or compositions thereof.
William DeMeo has been doing many posts in MathOverflow in re universal algebra. He will probably suggest the majority function on the set {0,1}, varieties which have a ternary or 4-place discriminator term, ternary groups, and the like. He may also point to places in the literature where your question has been raised.
Gerhard "Memory Not So Good Lately" Paseman, 2010.12.14