Are there items bigger than an aircraft section transported by air today?
According to Wikipedia, the An-225 is the world's largest cargo aircraft and it's transported both the heaviest and longest items of cargo ever carried by air:


  On 11 August 2009, the heaviest single cargo item ever sent via air
  freight was loaded onto the Antonov 225. At 16.23 metres (53.2 ft)
  long and 4.27 metres (14.0 ft) wide, its consignment, a generator for
  a gas power plant in Armenia along with its loading frame, weighed in
  at a record 189 tonnes (417,000 lb)
  
  [...]
  
  On 11 June 2010, the An-225 carried the world's longest piece of air
  cargo, when it flew two new 42-meter test wind turbine blades from
  Tianjin, China


It's also carried the Buran spacecraft (the 'Soviet space shuttle'), which was actually what the aircraft was originally built for.

The An-225 is still in operation and the operator gives some examples of large cargo that can be carried:


  The aircraft has the spacious cargo compartment with length of 43.32
  m, width of 6.4 m and height of 4.4 m, that allows carrying a variety
  of cargoes inside. For instance,
  
  
  sixteen standard aeronautical containers of UAC−10 type;
  50 cars;
  single piece of cargoes up to 200 t (turbines, generators, dump trucks − Belaz, Kamatsu, Euclid, etc.).