All non-empty finite sets of positive integers
GolfScript, 21 characters
;]]0{)\{.2$+.p}%\1}do

A GolfScript version which prints all generated sets. It basically does the same as my Python version although not by recursion but instead collecting all possible sets in an array.
;        // clear the stack
]]       // put [[]] on the stack - the array of generated sets 
            (initially an array with only the empty set)
0        // counter starts with zero
{        // start of infinite loop
  )      // increase counter
  \{     // map for each item of the array
    .    // duplicate item (i.e. this is a set)
    2$+  // append counter
    .p   // print the newly generated set
  }%\    // end of map =&gt; now the array contains all sets with max. up to counter
1} do    // end of infinite loop