Removing empty sets from lists

This works for any level (recursively):

{Andy, {}, {}, {}, {Jeff, {{}}, Tim}, {}, {Zach, {}}} //. {} -> Sequence[]
(*
 {Andy, {Jeff, Tim}, {Zach}}
*)

Or the cryptic

{Andy, {}, {}, {}, {Jeff, {{}}, Tim}, {}, {Zach, {}}} //. {} :> Unevaluated[## &[]]

Assuming "choose the nonempty sets" means to remove Nulls, this can be done with Select

list={Andy, {}, {}, {}, {Jeff, Tim}, {}, {Zach}};
Select[list, UnsameQ[#, {}] &]

{Andy, {Jeff, Tim}, {Zach}}

This is also a prime candidate for DeleteCases, here's the equivalent of belisarius method for empty lists nested just one level down:

DeleteCases[{Andy, {}, {}, {}, {Jeff, {{}}, Tim}, {}, {Zach, {}}}, {{} ...}, Infinity]

{Andy, {Jeff, Tim}, {Zach}}

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