How many adult childrn ages 21-34 live at home with parents?

Are you asking about the USA or some other group of countries? You
typed parents. Are both necessary or is one parent and 0 to 9 other
persons in the home ok? Did you intend to exclude situations in which
the adult child is defacto head of the family? How many days per year
is living at home? I'll guess ten million adult children in the USA,
lived at home last year 30 nights or more. Almost half were in college
or other training part or full time, part or all of last year.   Neil

A bit of trivia:

In Japan, stay-at-home adult children are labelled "parasaito
shinguru" or "parasite singles".

http://encyclopedia.thefreedictionary.com/Parasite+singles

I'm asking about the US only (although i loved the japanese
translation of the term!)  Don't care whetgher it's one or both
parents in the home = de facto head of family isn't an issue either -
i'm talking about situations where grown kid is dependent at least for
shelter, etc., on parent...and am not talking about kids in college
for some or all of the year or living at home while attending college
at least part-time...

I dont know the exact numbers, but i did find a usefull website that
may more acuratly adress what you want to know,
http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=27919

The most reliable information I could find was an intergenerational
survey conducted by Messineo and Wojtkiewicz (2004) that covered the
decades 1960, 1970, 1980 and 1990 (but NOT 2000). In addition,
Messineo and Wojtkiewicz surveyed 19-30 years-olds, not 21-34.
Moreover, the data is presented in percentages, not in absolute
numbers.

In other words, there is no survey that answers your question exactly. 

Messineo and Wojtkiewicz found that there is a significant rise in the
percentage of 19-30 year-olds who live with their paernts.

[Note: your question is about to expire. If you'd like me to publish
Messineo and Wojtkiewicz's findings and other information that I found
on the subject, it might be necessary for you to re-post the
question].