For example, I worked for a decade in the linux kernel and low-level userspace. Assembly definitely needed. I tracked down and fixed a bug in the glibc locking code, and you'd better believe assembly was required for that one. During that time I dealt with assembly for ARM, MIPS, powerpc, and x86, with both 32 and 64-bit flavours of most of those. But even there most of the time you're working in C, with as little as possible in assembly.
If you're working in the kernel or in really high-performance code then assembly can be useful. If you're working with experimental languages/compilers where the compilers might be flaky, then assembly can be useful. If you're working in Java/PHP/Python/Ruby/C# etc. then assembly is probably not all that useful.