Are there any issues in storing an Android battery? I want to buy a 2nd battery for my i9100 because the phone is getting old and I don't know if parts will be easily available a couple of years on (don't want to upgrade, I like it too much), but I've heard reports of batteries dying after being left in storage for extended periods. Is this true?
Should I just switch the 2 batteries around each time to preserve their life?
Unlike Ni-Cd and Ni-Mh batteries, Li-ion batteries primarily lose their capacity by calender time rather than by charge/discharge cycles.  It's simply a fact of the chemistry.  From the time the cell is assembled, it will lose capacity over time, regardless of whether it's in active use or sitting in a warehouse.

Stored unused, you're looking at up to 15-20% loss of capacity per year (pg 4, figure 5b) with the battery just sitting on a shelf.  Though this is more a worst-case scenario, as the battery is being stored at 35°.

To help prevent this capacity loss, you should store the battery cold.  In the paper above, storing the battery at 5° C (a few degrees warmer than an average kitchen fridge, which is ideally about 1.6° C) reduced the capacity loss rate by about half.

Putting the battery in a nice airtight bag (a small ziplock is good) is highly recommended for fridge storage to prevent unfortunate incidents relating to spills and condensation.