jQuery
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Code Link 1 Link 2 Link 3 Source Documentation:
$("#id1").append("<p>Additional content</p>");
$("#id2").replaceWith("<p>New content</p>");
$("#id3").remove();
MooTools
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Code Link 1 Link 2 Link 3 Source Documentation:
$("id1").grab(new Element("p", { html: "Additional content" }));
$(new Element("p", { html: "New content" })).replaces($("id2"));
$("id3").dispose();
The Dojo Toolkit
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Code Link 1 Link 2 Link 3 Source Documentation:
dojo.create("p", { innerHTML: "Additional content" }, "id1");
dojo.place(dojo.create("p", { innerHTML: "New content" }), "id2", "replace");
dojo.destroy("id3");
Prototype / Script.aculo.us
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Code Link 1 Link 2 Link 3 Source Documentation:
$("id1").insert("<p>Additional content</p>");
$("id2").replace("<p>New content</p>");
$("id3").remove();
Ext JS
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Code Link 1 Link 2 Link 3 Source Documentation:
Ext.DomHelper.append("id1", { tag: "p", html: "Additional content" });
Ext.DomHelper.overwrite("id2", { tag: "p", html: "New content" });
Ext.get("id3").remove();
Adobe Spry
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Code C Link 1 Source Documentation:
Spry.$$("#id1").forEach(function(e){
var n = document.createElement("p");
n.innerHTML = "Additional content";
e.appendChild(n);
});

Spry.$$("#id2").forEach(function(e){
var n = document.createElement("p");
n.innerHTML = "New content";
e.parentNode.replaceChild(n, e);
});

Spry.$$("#id3").forEach(function(e){
e.parentNode.removeChild(e);
});
BBC Glow
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Code Link 1 Link 2 Link 3 Source Documentation:
glow.dom.get("#id1").append("<p>Additional content</p>");
glow.dom.get("#id2").replaceWith("<p>New content</p>");
glow.dom.get("#id3").remove();
Yahoo! UI Library
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Code Link 1 Source Documentation:
Y.one("#id1").append("<p>Additional content</p>");
Y.one("#id2").insert("<p>New content</p>", "replace");
Y.one("#id3").remove();

 Matthias Schütz - Media Designer / Web Designer / Developer / Freelancer