What is the largest inductance value ever attained(in Henries)?
The largest inductor ever known to me was Fermi National Accelerator Lab's Tevatron magnet.  If memory serves it was 1000 Henries running continuously at 1400 DC Amperes.  Energy storage must have been right around 1 GigaJoule.  They had a "quench resistor" designed to burn off the energy in case the magnet would develop an open circuit.  The resistor (designed by my boss!) could be seen from space on Google Maps until not long ago.