Are these acceptable?
- Nov. 2nd, 2011
- Nov 2nd, 2011
- Nov 2, 2011
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All three are acceptable, as are other forms such as 2 Nov 2011, as found in the related stories list of UK newspaper the Guardian.
Only abbreviate where appropriate, otherwise write the longer form.
Which one you choose should be guided by your publication's style guide, if you have one, or just pick your own and be consistent.
I think none of those are acceptable in literate writing. In the first two, 2nd is a problem, and in the last two, the missing period is a problem. "Nov. 2, 2011" is an acceptable form, according to the "months" section near the end of an AP Style Guide webpage. (That guide drops the periods in the case of dates in tables.)