<p>I'd like to create a text field with a dropdown list that lets the user choose some predefined values. The user should also be able to type a new value or select a predefined one from a dropdown list. I know that I can use two widgets for that but in my app it would be more ergonomnic if it was unified in a one widget.</p>

<p>Is there a standard widget or do I have to use a third party javascript?</p>

<p>How about browser portability?</p>

I am not sure there is a way to do it automatically without javascript.
What you need is something which runs on the browser side to submit your form back to the server when they user makes a selection - hence, javascript.
Also, ensure you have an alternate means (i.e. a submit button) for those who have javascript turned off.
A good example:
Combo-Box Viewer
I had even a more sophisticated combo-box yesterday, with this
dhtmlxCombo
, using ajax to retrieve pertinent values amongst large quantity of data.