In the United States, are ultralights legally considered aircraft?
Yes, under FAA regulations, ultralight vehicles are considered to be aircraft.

14 CFR 1.1 states:


  Aircraft means a device that is used or intended to be used for flight in the air.


Ultralights are used or intended to be used for flight in the air, so they are aircraft.

14 CFR Part 103 defines the term "ultralight vehicle" and describes the rules for operating an ultralight vehicle. Although Part 103 avoids using the word "aircraft" to describe ultralight vehicles, nothing in Part 103 (or anywhere else) states that they are not aircraft.

It is true that ultralight vehicles are exempt from nearly all regulations governing aircraft. However, this isn't because ultralights aren't legally considered aircraft; it's because there are regulations which specifically make ultralights exempt from those regulations. For example:


Part 103, Section 7, states that


ultralight vehicles are not required to meet airworthiness standards,
pilots of ultralight vehicles are not required to have any kind of certificate, and
ultralight vehicles are not required to be registered.

Part 61, Section 51(j), states that pilots are only permitted to officially log flight time in aircraft that are registered (as well as military and public aircraft). Ultralights cannot be registered.
Part 91, Section 1(e), states that ultralight vehicles are exempt from Part 91 in its entirety. (If ultralight vehicles were not legally considered aircraft, then this paragraph would not need to exist!)


(Of course, a pilot may make logs of flights performed in ultralights, but the FAA does not recognize this time as "flight time".)

So, the FAA does consider ultralight vehicles to be aircraft. However, they are exempt from most—but not all—regulations which govern aircraft.