How can I detect pressing Enter on the keyboard using jQuery?

The whole point of jQuery is that you don’t have to worry about browser differences. I am pretty sure you can safely go with enter being 13 in all browsers. So with that in mind, you can do this:

$(document).on('keypress',function(e) {
    if(e.which == 13) {
        alert('You pressed enter!');
    }
});