x86-64 is a great architecture for many applications. It's cheap (due to volume), well-understood, has great compatibility, and is pretty much the best-supported architecture when it comes to software.
Edit: that being said, no, this doesn't have any embedded use today. Embedded x86 isn't 386 processors anymore. The typical scenario for an embedded x86-64 is "I need to drive this specific application and I want to leverage the Linux/FreeBSD/Windows environment for programming". That already puts you way ahead of the point where writing assembly code is useful performance-wise, and you probably don't want to put ASM code you downloaded off the Internet in a network-facing position :-).
Security is enough of a consideration that any well-established webserver without corporate or foundational backing is instantly unsuitable for serious use.