A new service plan was announced 04/2015, called SQL Azure Elastic database pool. As of today, it is still in preview mode, but pricing is available here -- make sure you click on Elastic Database button to see the prices.
With Elastic database pool the pricing model is as follows. First, you pay per pool, based on number of performance units you reserve for the pool (DTUs). Then you pay additionally for each database, which is part of the pool. The per-database price is quite small (currently around $1.26/mo), so most of your expenses will be a payments for DTUs, that are shared across all databases of your pool.
UPDATE:
As of May 2016, Azure SQL Database elastic pool is generally available. The pricing details are also updated. As of today, you can get up to 200 databases in Basic Tier for $149/month, which boils down to $0.745 per month per database.