Can a friend give you money that is not taxed?

Yes as long as it is a qualified gift according to the IRS gov website definition.

Any transfer to an individual, either directly or indirectly, where full consideration (measured in money or money's worth) is not received in return.

For tax year 2009 or 2010 one individual can gift to any other number of individuals up to $13,000 each without any reporting by either party each year.

The person who receives your gift does not have to report the gift to the IRS or pay gift or income tax on its value.

If you give any one person gifts in 2009 or 2010 that were valued at more than $13,000, you must report the total gifts to the Internal Revenue Service and may have to pay tax on the gifts each year.

For more information go to the IRS gov web site and use the search box for publication 950, Introduction to Estate and Gift Taxes, IRS Form 709 United States Gift Tax Return, and Instruction for Form 709.

The instructions are available at the IRS gov web site choose within Forms and Publications

However, what you call a gift and what the IRS defines as one may be different.