The Database Mirroring feature of SQL Server is going to die:
This feature will be removed in a future version of Microsoft SQL Server. Avoid using this feature in new development work, and plan to modify applications that currently use this feature. Use AlwaysOn Availability Groups instead.
Anyone knows when? What are my options for an High Availability (and quick recovery) database?
Mirroring isn't dead, and that concern isn't a very good reason to move away from it. As of SQL Server 2014 it's still there, so there's no cause for concern until you start to look at moving off of 2014 to a newer version. With 2014 only being 9 days old, that should be a while.
If you still want to see your other high availability options, look at the features each edition supports. Your choices will vary according to what you paid for. Here's a link to that document: http://msdn.microsoft.com/en-us/library/cc645993(v=sql.120).aspx
AlwaysOn will give you more functionality, but at the cost of purchasing Enterprise Edition.
As noted, mirroring is not dead. (At least not yet.) The general population doubts that Microsoft would totally abandon HA for Standard Edition.
However, there are other methods. In the SQL Server 2012 documentation when referring to mirroring it says: "If your edition of SQL Server does not support AlwaysOn Availability Groups, use log shipping."
There is plenty of instruction on using log shipping.
EDIT: You might read Kin's links at: SQL Server Log Shipping: File copy options?
Basic Availability Groups available in Standard Editions of SQL Servers 2016 forms a like to like replacement of Database Mirroring and has exact similar features.
Both available for Standard Editions Only Primary Replica Database will be accessible Databases cannot be failed over in groups as Basic AG can have only 1 DB per group
And Enterprise Editions obviously have the complete Availability Groups as a full fledged feature to provide HA.
Microsoft hasn't announce the retirement date of Database Mirroring hence it is expected to be in at least to of the future editions after SQL Server 2016.