Remove a HTML tag but keep the innerHtml

$('b').contents().unwrap();

This selects all <b> elements, then uses .contents() to target the text content of the <b>, then .unwrap() to remove its parent <b> element.

For the greatest performance, always go native:

var b = document.getElementsByTagName('b');

while(b.length) {
    var parent = b[ 0 ].parentNode;
    while( b[ 0 ].firstChild ) {
        parent.insertBefore(  b[ 0 ].firstChild, b[ 0 ] );
    }
     parent.removeChild( b[ 0 ] );
}

This will be much faster than any jQuery solution provided here.

You can also use .replaceWith(), like this:

$("b").replaceWith(function() { return $(this).contents(); });

Or if you know it's just a string:

$("b").replaceWith(function() { return this.innerHTML; });

This can make a big difference if you're unwrapping a lot of elements since either approach above is significantly faster than the cost of .unwrap().