The Customs and Border Protection website recommends that you register items before leaving the United States. I have known many people who have traveled out of the county and have had no issues with being asked to pay duty on items.
How serious should I actually take this tip? Are there certain countries I should be more or less worried about this?
Unless you are planning to bring back a trunks worth of stuff I don't think you should be worried about this.
The registration of these items is with US Customs that they don't charge you duties for when you come back but again if you are not bringing items that are not forbidden but don't sell in the United States (that would be a fairly short list) you may not need to declare them.
