This function is designed to protect against any interference with tags or attributes, focusing solely on text content.

function safeHtmlReplace(target, replacement, element) {    
    if (!element) element = document.body;    
    var nodes = element.childNodes;
    for (var n=0; n<nodes.length; n++) {
        if (nodes[n].nodeType == Node.TEXT_NODE) {
            var regex = new RegExp(target, 'gi');
            nodes[n].textContent = nodes[n].textContent.replace(regex, replacement);
        } else {
            safeHtmlReplace(target, replacement, nodes[n]);
        }
    }
}

safeHtmlReplace('a', 'r');

Bookmarklet version:

javascript:function htmlreplace(a,b,element){if(!element)element=document.body;var nodes=element.childNodes;for(var n=0;n<nodes.length;n++){if(nodes[n].nodeType==Node.TEXT_NODE){nodes[n].textContent=nodes[n].textContent.replace(new RegExp(a,'gi'),b);}else{htmlreplace(a,b,nodes[n]);}}}htmlreplace('old','new');

If you decide to update the innerHtml, be mindful that it can potentially disrupt any dom events currently in place on the page. Consider traversing the document to modify text instead:

function replaceOldWithNew(node) {
    node = node || document.body;
    if (node.nodeType == 3) {
        // Text node
        node.nodeValue = node.nodeValue.split('old').join('new');
    } else {
        var nodes = node.childNodes;
        if (nodes) {
            var i = nodes.length;
            while (i--) replaceOldWithNew(nodes[i]);
        }
    }
}

replaceOldWithNew();

When there is no need for pattern matching, using split/join is faster than "replace". However, if pattern matching is required, utilize "replace" with a regex like this:

node.nodeValue = node.nodeValue.replace(/(?:dog|cat)(s?)/, 'buffalo$1');

To use it as a bookmarklet, here's the code snippet:

javascript:function replaceOldWithNew(node){node=node||document.body;if(node.nodeType==3){node.nodeValue=node.nodeValue.split('old').join('new');}else{var nodes=node.childNodes;if(nodes){var i=nodes.length;while(i--)replaceOldWithNew(nodes[i]);}}}replaceOldWithNew();

To ensure compatibility with older browsers, it is necessary to make a slight adjustment by changing Node.TEXT_NODE to 3 and updating node.textContent to node.nodeValue; the final function will appear as follows:

function replaceHTMLContent(targetString, replacementString, element) {    
    if (!element) element = document.body;    
    var nodes = element.childNodes;
    for (var n=0; n<nodes.length; n++) {
        if (nodes[n].nodeType == 3) { //Node.TEXT_NODE == 3
            var regex = new RegExp(targetString, 'gi');
            nodes[n].nodeValue = nodes[n].nodeValue.replace(regex, replacementString);
        } else {
            replaceHTMLContent(targetString, replacementString, nodes[n]);
        }
    }
}

Here is a straightforward method using jQuery:

`javascript: var changeText = function(){$("body").html($("body").html().replace(/old/g,'new')); return;}; changeText();`

If you prefer to avoid jQuery, you can use the following code:

`javascript:function changeText(){document.body.innerHTML=document.body.innerHTML.replace(/old/g, "new" ); return;}; changeText();`

Remember that having the function return nothing is crucial to prevent the browser from redirecting after running the bookmarklet.

Here is an alternative recursive method to replace text:

function updateText(original, replacement, element){ 
  element = element || document.body; 

  var children = element.childNodes, index = 0;

  while(element = children[index]){ 
    if (element.nodeType == Node.TEXT_NODE){ 
      element.textContent = element.textContent.replace(original, replacement); 
    } else { 
      updateText(original, replacement, element); 
    } 
    index++; 
  } 
}

To make it more concise for a bookmarklet:

javascript:function updateText(o,r,e){e=e||document.body;var c=e.childNodes,i=0;while(e=c[i]){if(e.nodeType==Node.TEXT_NODE){e.textContent=e.textContent.replace(o,r);}else{updateText(o,r,e);};i++;}};updateText('original','replacement');

Alright, I am compiling all the valuable information that individuals are contributing into one comprehensive response.

Check out sixthgear's jQuery code below, which has been customized to be portable (sourcing jQuery from the well-known G) and condensed into a bookmarklet:

javascript:var scrEl=document.createElement('script');scrEl.setAttribute('language','javascript');scrEl.setAttribute('type','text/javascript');scrEl.setAttribute('src','http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js');function htmlreplace(a,b,element){if(!element)element=document.body;var nodes=$(element).contents().each(function(){if(this.nodeType==Node.TEXT_NODE){var r=new RegExp(a,'gi');this.textContent=this.textContent.replace(r,b);}else{htmlreplace(a,b,this);}};}htmlreplace('old','new');

Please note that 'old' can either be a 'string literal' or a 'reg[Ee]x'.

In my opinion, sixthgear's solution stands as the strongest answer, especially with the enhancements I have added. None of the other responses bring anything new to the table compared to this one. Using jQuery ensures exceptional cross-browser compatibility. Additionally, let's be real, I'm just too lazy for anything else. This post is community wiki, so enjoy!