What is the most powerful and most expensive type of computer available?

As of June 18th, 2012, the most powerful supercomputer in the world is Sequoia, an IBM BlueGene/Q system installed at the Lawrence Livermore National Laboratory in Livermore, CA, USA. It employes 1,572,864 individual processor cores to achieve a record 16.32 petaflops (that's 16,320,000,000,000,000 or sixteen million billion floating point calculations per second).

Approximate cost: USD $250,000,000.

Sources: top500.org; llnl.gov