For example, are there inductors with values in terms of kilo-henries or even mega-henries? 1 Henry inductors are not all that easy to find.
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.
What is the largest inductance value ever attained(in Henry's)?
The magnetic permeability of free space is 1.2566370614…×10−6 henries per metre and the universe is pretty big. "What" you might possibly say and I would say that radio waves (and light) are carried vast distances between far-away galaxies so this "inductance" is being used to convey energy we can see and detect therefore it exists.
Between earth and the sun (93 Million miles or 150,000,000 km) I estimate the inductance to be 188,000 henries.
I can't compete with the Universe (that's cheating anyway), but it's fairly easy to buy 25H inductors for power supply smoothing. The audiophile guys do this all the time for their valve amps.
Inductance is a way to transfer power from one bit of metal to another. So look at transformers. Clearly power rating is closely related to inductance. I can't find concrete evidence of anything bigger than 1200 MVA, but see this Wiki page. It lists the largest inductance at ~1300H for a 3000MW transformer. ABB do some large ones.
So we need another question: What's the biggest single transformer, and what's the power /inductance equation?
Not sure about those but I just measured the inductance of a Tesla Model S rear drive AC inductance motor and it's somewhere between 20H and 25H across one phase. I got 23H but it was a really rough measurement. This means it would be around 70H for the 3 phases.
It's not the largest admittedly, but it's interesting to me so I thought I'd add it as a real world thing.