I know that you cannot sail into the
USA on a visa waiver on a private boat and am fairly certain that the
rule also applies to leaving the
USA - which would mean you need a US tourist visa in your passport in order to sail your new acquisition out of the country. Usually the airlines will not allow you to fly to the USA on a one-way ticket unless you are a US resident. You can get around this by
purchasing a round-trip ticket that is fully refundable and getting your
money back for the unused portion, but those tickets tend to be quite pricey.
Addendum - I read on a German forum some posts by a gent who did this, entered the USA on a visa waiver program and wanted to depart on a boat that he had purchased. After mailing and talking with the German embassy, the US Consulate in
Germany and homeland
security he could not get a staight answer on whether or not this was possible. In the end it turns out that the all-important I-94 issued by airlines is different from that issued when arriving at a port and that there would probably be issues when checking out of the USA with the "wrong" I-94. I would want to have some US agency clarify this in writing before attempting to leave on your boat without having entered on a visa.
Of course the Tourist Visa is pretty easy to get as an EU-citizen, in my case the assigned date for the visa interview took several weeks and then they kept my passport for a week before it was mailed back (with a visa). So if you have enough time to prepare then just go and get the visa so that you won't have any problems.