You can define the Y combinator, and therefore recursion quite happily (if not very efficiently) using S and K.
I believe there are also approaches that use as single universal combinator - but I can't find any good references to these - I'd be quite interested to see definitions of S and K in terms of a single universal combinator.
They recover the S and K by applying U to itself in interesting ways, but that's like saying 'this tool is so universal, you can use it as a hammer and a chisel by banging one instance of the tool with another tool just like it'.
That's not a very mathematical way of putting it I guess but I believe that is more or less the spirit of it.
http://en.wikipedia.org/wiki/SKI_combinator_calculus
You can define the Y combinator, and therefore recursion quite happily (if not very efficiently) using S and K.
I believe there are also approaches that use as single universal combinator - but I can't find any good references to these - I'd be quite interested to see definitions of S and K in terms of a single universal combinator.