I think one of the values of assembly languages today that is often overlooked is the didactic value. I would contend that an assembly language is the best entry language for someone who has never programmed before. Why? Because it is simple and bare. In assembly you have basically three elements: Registers, opcodes and memory addresses. Learn how to mix-and-match those three basic elements and you can do a lot. Now take C for instance, for someone who has never coded before, C is pretty darn complex. Right out of the bat you have functions,
#includes, macros, structs and more. That's a lot to take in. Go to a higher level language like Java and then you have the whole concept of classes and objects that must be understood beforehand. My personal opinion is that when learning something new, I prefer to start small. This is why I think assembly is an overlooked didactic tool.
Now on practical aspects, when you get the job of optimizing code, there is also value in being able to read and understand assembly. A lot of optimizations are about reading compiled code and seeing where the compiler is screwing up and how to change your higher level code in a way to allow the compiler to generate faster machine code.
Specifically on game programming, if you look back at the 80s and 90s, there was a lot of assembly programming going on on games and other high performance software, mainly because it was a pressing necessity. Most games used assembly code to be able to access special hardware features, like vectorization instructions such as MMX/SSE/AltiVec/etc. Today, these vectorization instructions are available as compiler intrinsics, so there is little gain in writing them using assembly.
Another issue that is driving game programmers away from assembly is portability. Not many studios can afford to release their games on a single platform these days. You need to write portable code, so assembly is only used as a last resort.
Last-gen Consoles like the PS3 still saw quite a bit of assembly programming, mainly due to its special hardware features that could not be accessed in any other way. But next-gen hardware is a lot closer to desktop PCs in architecture and performance, so again, assembly is loosing space there.