There are many business applications still running on Cobol, but new developers would never base their career solely around learning Cobol. Even for developers who are working with more modern languages and methodologies, specializing in a single technology isn't the best basis for a career.
Besides the fact that technology changes rapidly (Cobol aside!), developers with a skill set across the technology stack are more valuable to their organization. These developers can step up and pitch in wherever help is needed, and their understanding of the challenges of different technologies provides a foundation for working in architecture, project lead, or managerial roles in addition to a varied programming career.
Software ultimately runs on physical facilities, so understanding the limitations of hardware and networks helps engineers make appropriate design decisions. Projects can either take advantage of, or be limited by, the specific operating system they are running on, so understanding this is key. Network configurations raise performance issues and security concerns, especially with growing use of the cloud. Mobile devices offer unique challenges as well. Applications won't succeed unless developers understand these issues and handle them appropriately.
There are fads and trends in programming, so while knowing a specific language is helpful for a while, having a solid foundation in good software engineering practices is more important. Developers need to fully grasp the concepts of object-oriented design in order to write reusable code that speeds projects. Debugging skills are often overlooked, but crucial. So is the ability to reverse engineer and work with existing code, so developers should practice reading and analyzing code they didn't write.
Ultimately, most applications require manipulating data, so developers should be comfortable with a variety of databases. Developers should be able to write SQL queries and work with stored procedures. Although many data-dependent projects will have DBAs to fine-tune the database, developers should be comfortable with the basics of database design and performance tuning. Because "big data" is increasing in importance, developers should learn how to work with very large datasets.
Understand Front Ends
Applications aren't useful until someone uses them, so developers need to understand what makes an effective front end. A designer may polish the look and feel, but developers should understand what works well on different platforms – thick clients still exist, and web applications and mobile apps present different challenges.