TITLE: "Natural" generating sets for symmetric groups
QUESTION [15 upvotes]: The symmetric group on $n$ letters has 
many sets of generators. Some of them are more natural than others, eg the
set $(i,i+1)$ of adjacent transpositions (natural with respect to the type A Weyl group), the set of all shuffles (permutations corresponding to "card-shuffles", ie $\sigma(1),\sigma(2),\dots,$ contains at most two increasing subsequences) perhaps also sets consisting of conjugacy
classes (preferably of signature $-1$ in order to avoid a stupid mistake).
Which other sets of generators of symmetric groups occur in a natural way?

REPLY [2 votes]: Another answer from a combinatorial point of view: the set of all transpositions is a generating set for $S_n$. Obviously this is a huge overkill. But a nice thing about including all transpositions is now your generating set is closed under conjugation. In fact, this generating set is used to define the so-called absolute order or reflection order (which applies more generally to any Coxeter group); the absolute order has as its Hasse diagram the Cayley graph with respect to the transpositions as generating set. Absolute order comes up for instance in Coxeter-Catalan combinatorics, a currently popular topic.