Interactive songs

Songs are good for communication (language), community, cognitive and identity.
You can't make a child sit and sing or do any activity, it needs to be something that they enjoy.
Some interactive songs for children are as follows:

Aiken Drum - Children can add their own words to sing (eg. "His pants were made out of sausages..." and go back to the chorus).
A Ram Sam Sam - A Turkish song.
The Lion Sleeps Tonight - I love this song! Catchy, good vocals, and the cartoon animals will be popular with children, too.
Backe, Backe Kuchen (Cooking Cake) - German. This is a great one to teach your children another language (if you don't already speak it), and it teaches them how to bake a simple cake.

Here is the sheet music.

"Backe, Backe Kucken." Source: Catch a Song. Deanna Hoermann and Doreen Bridges (1985. Reprinted. 1992 & 1994)

The Drover's Dream - This is good for children 4 years and over. You can try it with 3 year olds, but I'd imagine more 4.
The Farmer in the Well - The song's very good and very interactive. Maybe not very suitable for younger children (younger than 3), but you can do this activity with 3+.
Form a circle
One child is selected and skips inside the circle while the first verse of the song is sung.
During the second verse, the 'farmer' selects another child to be his wife (if the 'farmer' is a female, change 'wife' to 'husband').
Both skip around the circle.
More children are selected for each part as each verse is sung, ending with the cheese standing alone.
The children forming the circle can change the beat or rhythm of the song as it is performed.