What Current Continuous SQL Server Backup Solutions Are there?
Well, you can keep using mirroring. "Deprecated" does not mean "doesn't work any more" - it just means that, at some point in the future, it won't be supported when you move to some version > 2012 (probably at least 3 versions later, maybe more given the backlash this announcement has caused). 

By then, I am sure they will have a replacement for mirroring for Standard Edition, or will have simply deprecated Standard Edition, too. At that time, not today, you can make a decision to (a) use the replacement (or upgrade to Enterprise), (b) stay on the version you're on, or (c) switch to a different RDBMS.

Deprecation isn't exactly the jump-the-ship right now or sink ultimatum a lot of people infer. For example, they deprecated "statements that don't end with semi-colons" back in 2008. Are you adding semi-colons to every statement you write, today, on current versions of SQL Server? Nope, I really doubt it. Do you need to abandon mirroring this instant, or even in the next three years? Nope, not even close.