Question

Here’s a fiddle with a working Bootstrap carousel.
http://jsfiddle.net/jeykeu/5TDff/

And here’s the official documentation which tells nothing about event usage.
http://twitter.github.com/bootstrap/javascript.html#carousel

I thought this would work but no:

     $('#carousel').bind('slide',function(){
            alert("Slide Event");
    });

Answer 1

Based on your fiddle #carousel is wrong. It should be #myCarousel.

Updated Example:

$('#myCarousel').carousel({
    interval: 2000
});

// Could be slid or slide (slide happens before animation, slid happens after)
$('#myCarousel').on('slid', function() {
    alert("Slide Event");
});​

http://jsfiddle.net/infiniteloops/wPF3n/

With Bootstrap 3

http://jsfiddle.net/infiniteloops/wPF3n/252/