There are already at least three methods already in use: batteries, flywheels and thermal (see http://www.scientificamerican.com/article.cfm?id=how-to-use-solar-energy-at-night).

Unless some form of magnetic storage offered a clear advantage over these three, I can’t see any reason to pursue it.

Apart from what Mike mentioned, there are some really nifty capacitors nowadays, and in fact superconducting solenoids can store energy electromagnetically. Also, among mechanical methods there are some very large-scale possibilities by displacing seawater or compressing gas.

The idea that intermittent energy sources such as solar,  wind and wave won't work, is a favourite canard of the ignorant and obstructive. We could easily store enough  enargy to run every major city on Earth if only there were the political and short-term financial will, and do it without significant pollution or environmental footprint.

The entire problem revolves around energy density in the storage medium. National Grid UK has a few energy storage facilities which basically consist of pumping a lake from the bottom of a mountain to the top with any spare power (not too useful in Norfolk, but good in Scotland and Wales where wind and tidal need storage). Using natural materials (like pumping 10 million tons of fresh water uphill by 300 metres from Loch Awe to Loch Cruachan) dwarfs any technology solution like flywheels and phase-change materials.

Most conventional power stations need a fairly long time to respond to demand (gas turbine 10 mins, oil-fired 2 hours, coal-fired 4 hours, nuclear 24 hours) because of the thermal lag and thermal stress issues. The great advantage of stored energy systems is a much faster response to unanticipated demand or sudden supply failures. Pumped water response time to demand is around 10 seconds.