Whether or not you can use a logo for your company's trademark raises both copyright issues and trademark issues.
Copyright: Logos are protectable under copyright law. The rule is that you cannot lawfully use a logo that you did not create unless the logo is in the public domain or you purchase a license to use the logo. There have been many, many images of "Uncle Sam" created throughout the years. The most famous is the "I Want You" poster published in 1916 by James Flagg. Because the copyright to all works of authorship created during or before 1921 are now in the public domain, anyone can reproduce, distribute, or display that particular poster or create other works that are based on the poster. There are, however, many other images of "Uncle Sam" that were created after 1921 and so many of them are still protected under copyright law. In short, whether you can lawfully use a particular image of "Uncle Sam" depends on which image you use.
Note that while the federal government cannot own the copyright in the works of authorship that it creates directly, it certainly does own the copyright in the works that it commissions from others (such as reports, architectural plans, audiovisual works, etc.). The federal government did not create nor commission the original image of "Uncle Sam" and so plays no part in the analysis of whether you can use that image as a trademark.
Trademark: While the copyright in the "I Want You" poster (and therefore its particular image of "Uncle Sam") has expired, that does not mean that a person has the unfettered right to use that "Uncle Sam" image as a trademark. A quick search of the US Trademark Office database reveals that quite a number of companies already use the "Uncle Sam" image as a trademark. Just like any other trademark use analysis, you need to contact a trademark attorney who will have a trademark search performed and will then, and only then, determine whether your use of the "Uncle Sam" image would be lawful in light of all the other user's of that image.
