The software security community has a subsection that focuses on the security of compiled binaries, where understanding assembly has many uses. These uses include binary reverse engineering and proof-of-concept exploit development to demonstrate the severity of a vulnerability.
If these do sound interesting to you, I'd recommend looking into capture the flag (CTF) competitions, and trying reverse engineering or binary exploitation (pwn) challenges. PicoCTF [1] is an entry-level platform that hosts challenges and has references to learning resources - I believe there's a sequence on assembly in the learning resources.
Aside, I also find it useful to know assembly when debugging C/C++ code, as others have suggested.