It supposedly doesn't actually record until it hears the trigger word (alexa, unless you set it up to respond to amazon, computer, or echo), and then records what's said immediately after.
From what I've observed, that is the case. I haven't seen any network activity from it until the wake word has been said.
However, it can be used to eavesdrop by someone with the correct tools (by NSA, hackers, etc). But, so can your phone, your tablet, your laptop, your tv, and many other devices around you. Not to mention the old fashioned ways of eavesdropping. Cell phones are probably the worst, since they can provide so much -- phone convos, messaging transcripts, email logs, recordings of everything said in vicinity of phone, logs of everywhere you went, logs of everything you looked at online, etc.
Anyway, I figure there's lots more interesting folks out there than me for them to listen in on