Soon I will have the pleasant duty of leading an amateur choir at a two-week summer camp. I am looking for warming up pieces that are easy, but fun. It should be possible to learn them without having to read the sheet music, but also a bit more advanced singers should have fun.
I've found rounds especially good as warm-up pieces, as they can be taught to a mixed ability group without sheet music (and it doesn't matter what your ratio of male to female singers is!).
There are some excellent rounds and simple part-songs in the Voiceworks series of books (Peter Hunt) - my favourites are in Voiceworks 2 and include:
Ba-nu-wa (African round, has a particularly good final line)
Chicka Hanka (which you can keep building on over a period of time, adding more improvised noises, bass line etc) - a pdf of this song is at http://ukcatalogue.oup.com/product/music/series/choralseries/vw/9780193435506.do?sortby=bookTitleAscend
There's a girl that I love (a round with a punchline)
Online you'll find various campfire songs, and these would also work well as warm-up pieces. These two sites (as an example) have midi to help you learn the songs:
Sing for Pleasure also produce some good books on rounds and simple part-songs: http://www.singforpleasure.org.uk/resources/publications.php I've made particular use out of their 'Round and Round' book.
As another option, you could use well-loved pop songs or musical theatre pieces to get everyone buzzing, singing in unison or simple two/three part harmony. Examples that spring to mind are 'Do you hear the people sing' from Les Miserables, 'Do Re Mi' from The Sound of Music, and 'Let It Be' by The Beatles.