What's the proper value for a checked attribute of an HTML checkbox?

Strictly speaking, you should put something that makes sense - according to the spec here, the most correct version is:

<input name=name id=id type=checkbox checked=checked>

For HTML, you can also use the empty attribute syntax, checked="", or even simply checked (for stricter XHTML, this is not supported).

Effectively, however, most browsers will support just about any value between the quotes. All of the following will be checked:

<input name=name id=id type=checkbox checked>
<input name=name id=id type=checkbox checked="">
<input name=name id=id type=checkbox checked="yes">
<input name=name id=id type=checkbox checked="blue">
<input name=name id=id type=checkbox checked="false">

And only the following will be unchecked:

<input name=name id=id type=checkbox>

See also this similar question on disabled="disabled".

HTML5 spec:

http://www.w3.org/TR/html5/forms.html#attr-input-checked :

The disabled content attribute is a boolean attribute.

http://www.w3.org/TR/html5/infrastructure.html#boolean-attributes :

The presence of a boolean attribute on an element represents the true value, and the absence of the attribute represents the false value.

If the attribute is present, its value must either be the empty string or a value that is an ASCII case-insensitive match for the attribute's canonical name, with no leading or trailing whitespace.

Conclusion:

The following are valid, equivalent and true:

<input type="checkbox" checked />
<input type="checkbox" checked="" />
<input type="checkbox" checked="checked" />
<input type="checkbox" checked="ChEcKeD" />

The following are invalid:

<input type="checkbox" checked="0" />
<input type="checkbox" checked="1" />
<input type="checkbox" checked="false" />
<input type="checkbox" checked="true" />

The absence of the attribute is the only valid syntax for false:

<input />

Recommendation

If you care about writing valid XHTML, use checked="checked", since <input checked> is invalid XHTML (but valid HTML) and other alternatives are less readable. Else, just use <input checked> as it is shorter.

<input ... checked />
<input ... checked="checked" />

Those are equally valid. And in JavaScript:

input.checked = true;
input.setAttribute("checked");
input.setAttribute("checked","checked");