What's the best method to responsibly dispose of used alkaline batteries?
In the UK (and most, if not all, of the EU):


some supermarkets have recycling bins for small batteries. 
Every community has a household waste recycling centre with containers for old batteries (including both lead-acid car batteries and small appliance batteries like AA batteries).




EU Directive 206/66/EC says


  In order to protect the environment, waste batteries and
  accumulators should be collected. For portable batteries
  and accumulators, collection schemes achieving a high
  collection rate should be established. This means setting
  up collection schemes so that end-users can discard all
  waste portable batteries and accumulators conveniently
  and free of charge