The HTML 4.01 standard allows for one situation where a form field such as input is allowed to be included in your HTML without its being nested inside a form tag. In all circumstances except where this particular exception criteria is met your form fields such as input, button, textarea, and select all need to be nested inside a block level tag such as a div or fieldset which in turn needs to be nested inside the form tag. Note that none of the HTML validators will produce an error if you do not apply the required nesting since none of them actually test for any of the standards that involve tag nesting more than one level deep. This is a flaw in the validators where just because the page passed validation doesn't necessarily mean that it is actually valid.
We can therefore say that while the standards actually allow for a form field to not be nested inside a form under certain specific circumstances that there are almost no circumstances where it would be appropriate to do so.
This article written by Stephen Chapman, Felgall Pty Ltd.