Alan provides a good list of alternatives to duple improper dances. At the various dances
here in New Hampshire, we will always do at least one of those alternatives at every
dance, and more often 3 or 4 or more.
Chorus Jig is the favorite proper dance (happens every Monday night at the Nelson dance),
but there are others from time to time, as well. Also triple-minors like Sackett's
Harbor, or Money Musk are called very regularly.  Mixers, both circle and scatter, are
also danced quite often, especially when there is a larger proportion of new dancers, as
dancing with a larger number of alternate partners helps the learnig process proceed more
quickly. There are also a number of callers here who like to include some squares,
espcially the older New England variety of singing squares, such as Nellie Gray, Smoke on
the Water, Just Because, and the Auctioneer.
Rich.
Alan Winston - SSRL Central Computing remarked on 8/13/2011 7:05 AM:
  John wrote:
  In a recent post I defined a contra dance as:
 - longways for as many as will
 - first couples Improper, or Becket formation
 - flowing choreography
 - no-one stationary for more than 16 beats (e.g. First Couple Balance&
 Swing, finish facing down to make Lines of Four)
 - containing at least one swing
 - 95% of the moves to be from a set of well-know moves that they know
 already 
 (And I would add that most of those figures are connected; dancers are
very
 rarely asked to go on a track by themselves.)
  Is that what most Americans understand by a
"contra dance"? 
 Yes.
  I asked:
 Are you allowed to do Proper dances at a "contra dance"?  Or a
 four-couple dance that has all the other characteristics listed above?
 Or a Sicilian Circle (space allowing)?
 But got no answer. 
 It depends somewhat on the community.  The big-city (modern urban contra) scene
 tends to devolve toward longways contra, but charismatic, opinionated, and good
 callers can make a difference.
 At contra dances in the San Francisco Bay Area I have seen:
   - squares (and many people sit down for them)
   - triplets (and many people complain about gimmicks)
   - circle mixers
   - four-face-four
   - proper contras (rarely)
   - triple-minor contras (Sackett's Harbor - but not in the last 10 years)
   - scatter mixers
   - couple dances: waltz, polka, hambo
 and at contra dance camps/weekends I've also seen
   - grid squares
   - Appalachian big circle figures
  Taking it a step further - this is a popular
dance over here in the UK:
 Childgrove (Playford 1701)
 A1:       Partner Siding; Partner Dosido
 A2:       Neighbour Siding; Neighbour Dosido
 B1:       Neighbour Two-Hand Turn 1&  1/2 (skip step)
              Partner Two-Hand Turn
 B2:       #1s Full Figure Eight up through the #2s (who can cast to turn
 it into a double-figure-eight if they like) (skip step) 
  It has all the characteristics defined above
apart from the swing being
 replaced by a skipped two-hand turn.  And of course the moves may not be
 all familiar to contra dancers.  If I called that at an American contra
 dance, to great music from a live band, what reaction would I get? 
 Depends on the crowd, but it's not something I'd be inclined to try except
 under very specific circumstances.
 (Except for crossover English dancers, you'd have to teach siding, your dosido
 would end up with a lot of twirls in it, and you'd have to teach the figure
 eight from zero, the two-hand turns at different speeds might be challenging.)
 If the band plays it as they would for an English dance, the contra dancers
 won't know what to do with it (as I know from sad experience).  If you play it
 like a contra dance tune, you won't get an English dance out of it.
 (I bet Cammy Kaynor could sell it to his dancers, though.)
 I was recently at a contra dance camp which had a late-night "Trash English"
 session.  Bluesy, swingy, low-down versions of English tunes, and dancers
 responding to them with contra and swing body language and flourishes, using
 the original figures as an armature on which to hang those variations.  Great
 music, strong dancers, really fun.  Childgrove would have been fine there.
 Hope that helps somewhat.
 -- Alan