Update:

I have outlined some basic performance tests for each of these 6 methods over 1000 runs. getElementsByTagName is the fastest but it does a half-assed job, as it does not select all elements, but only one particular type of tag ( i think p) and blindly assumes that its firstChild is a text element. It might be little flawed but its there for demonstration purpose and comparing its performance to TreeWalker. Run the tests yourselves on jsfiddle to see the results.

1. Using a TreeWalker
2. Custom Iterative Traversal
3. Custom Recursive Traversal
4. Xpath query
5. querySelectorAll
6. getElementsByTagName

Let's assume for a moment that there is a method that allows you to get all Text nodes natively. You would still have to traverse each resulting text node and call node.nodeValue to get the actual text as you would do with any DOM Node. So the issue of performance is not with iterating through text nodes, but iterating through all nodes that are not text and checking their type. I would argue (based on the results) that TreeWalker performs just as fast as getElementsByTagName, if not faster (even with getElementsByTagName playing handicapped).

Ran each test 1000 times.Method                  Total ms        Average ms--------------------------------------------------document.TreeWalker          301            0.301Iterative Traverser          769            0.769Recursive Traverser         7352            7.352XPath query                 1849            1.849querySelectorAll            1725            1.725getElementsByTagName         212            0.212

Source for each method:

TreeWalker

function nativeTreeWalker() {    var walker = document.createTreeWalker(        document.body,         NodeFilter.SHOW_TEXT,         null,         false    );    var node;    var textNodes = [];    while(node = walker.nextNode()) {        textNodes.push(node.nodeValue);    }}

Recursive Tree Traversal

function customRecursiveTreeWalker() {    var result = [];    (function findTextNodes(current) {        for(var i = 0; i < current.childNodes.length; i++) {            var child = current.childNodes[i];            if(child.nodeType == 3) {                result.push(child.nodeValue);            }            else {                findTextNodes(child);            }        }    })(document.body);}

Iterative Tree Traversal

function customIterativeTreeWalker() {    var result = [];    var root = document.body;    var node = root.childNodes[0];    while(node != null) {        if(node.nodeType == 3) { /* Fixed a bug here. Thanks @theazureshadow */            result.push(node.nodeValue);        }        if(node.hasChildNodes()) {            node = node.firstChild;        }        else {            while(node.nextSibling == null && node != root) {                node = node.parentNode;            }            node = node.nextSibling;        }    }}

querySelectorAll

function nativeSelector() {    var elements = document.querySelectorAll("body, body *"); /* Fixed a bug here. Thanks @theazureshadow */    var results = [];    var child;    for(var i = 0; i < elements.length; i++) {        child = elements[i].childNodes[0];        if(elements[i].hasChildNodes() && child.nodeType == 3) {            results.push(child.nodeValue);        }    }}

getElementsByTagName (handicap)

function getElementsByTagName() {    var elements = document.getElementsByTagName("p");    var results = [];    for(var i = 0; i < elements.length; i++) {        results.push(elements[i].childNodes[0].nodeValue);    }}

XPath

function xpathSelector() {    var xpathResult = document.evaluate(        "//*/text()",         document,         null,         XPathResult.ORDERED_NODE_ITERATOR_TYPE,         null    );    var results = [], res;    while(res = xpathResult.iterateNext()) {        results.push(res.nodeValue);  /* Fixed a bug here. Thanks @theazureshadow */    }}

Also, you might find this discussion helpful - http://bytes.com/topic/javascript/answers/153239-how-do-i-get-elements-text-node

Here's a modern Iterator version of the fastest TreeWalker method:

function getTextNodesIterator(el) { // Returns an iterable TreeWalker    const walker = document.createTreeWalker(el, NodeFilter.SHOW_TEXT);    walker[Symbol.iterator] = () => ({        next() {            const value = walker.nextNode();            return {value, done: !value};        }    });    return walker;}

Usage:

for (const textNode of getTextNodesIterator(document.body)) {    console.log(textNode)}

Safer version

Using the iterator directly might get stuck if you move the nodes around while looping. This is safer, it returns an array:

function getTextNodes(el) { // Returns an array of Text nodes    const walker = document.createTreeWalker(el, NodeFilter.SHOW_TEXT);    const nodes = [];    while (walker.nextNode()) {        nodes.push(walker.currentNode);    }    return nodes;}

I know you specifically asked for a collection, but if you just meant that informally and didn't care if they were all joined together into one big string, you can use:

var allTextAsString = document.documentElement.textContent || document.documentElement.innerText;

...with the first item being the DOM3 standard approach. Note however that innerText appears to exclude script or style tag contents in implementations that support it (at least IE and Chrome) while textContent includes them (in Firefox and Chrome).