What classifies as an ultralight vehicle?
A typical ultralight looks like this, although there are plenty of different designs:



Source: wikimedia.org

Ultralights in the US are defined and regulated by 14 CFR 103. The definition in 103.1 is:


  For the purposes of this part, an ultralight vehicle is a vehicle
  that:
  
  (a) Is used or intended to be used for manned operation in the air by
  a single occupant;
  
  (b) Is used or intended to be used for recreation or sport purposes
  only;
  
  (c) Does not have any U.S. or foreign airworthiness certificate; and
  
  (d) If unpowered, weighs less than 155 pounds; or
  
  (e) If powered:
  
  (1) Weighs less than 254 pounds empty weight, excluding floats and
  safety devices which are intended for deployment in a potentially
  catastrophic situation;
  
  (2) Has a fuel capacity not exceeding 5 U.S. gallons;
  
  (3) Is not capable of more than 55 knots calibrated airspeed at full
  power in level flight; and
  
  (4) Has a power-off stall speed which does not exceed 24 knots
  calibrated airspeed.


And 103.7(b) says:


  (b) Notwithstanding any other section pertaining to airman
  certification, operators of ultralight vehicles are not required to
  meet any aeronautical knowledge, age, or experience requirements to
  operate those vehicles or to have airman or medical certificates.


But, just because you can fly an ultralight without any license or training doesn't mean it's a good idea! You should definitely look into local ultralight clubs to help get you started safely. For example, the EAA has a lot of members who fly (and sometimes build) ultralights and they have some useful information on getting started.