I checked the last several emails I've received from Amazon, and they all end with "Sincerely, Amazon.com" and the "Amazon.com" portion is ALWAYS a link although it isn't underlined. Is the OP's email suspicious? Yes. Is it a fake? Maybe, but then again Amazon is known for being quirky and sending out strange emails. To be safe, always delete such emails then later enter your account the normal way and change the password.

As far as security breaches go, I've had Adobe, T-Mobile, and the U.S. Office of Personnel Management all get hacked and my data possibly compromised in each of those cases, so always be suspicious.