I agree with those who ask: what kind of programming do you want to do?
If Perl is one of the best languages for that type of programming, learn it. (CGI, ETL, database publishing, text processing, system administration, etc.)
If not, there is a second reason to learn Perl: having a complete toolset. All programmers should learn at least one language or tool in these bread and butter areas:
1) database access (SQL is a must, Perl has excellent DBI/DBD access to multiple databases)
2) text processing (Perl is a winner here)
3) GUI (Java/Swing, C#, VB, JavaScript/HTML/CSS, ActionScript 3, take your pick)
4) ETL (Perl is great here, XML is necessary, XSLT annoying but useful, also tools like Informatica, but Java has great open source libraries for reading MS Office documents)
5) Scripting (either learn Perl which is nearly cross-platform, or choose one dictated by your OS, like DOS CMD, Unix bash/csh/tcsh etc, MAC's scripting technologies)
6) OO programming (Java, C++, C#, and even Perl)
7) Internet communication (Java, C#, etc.)
I am not paid to be an XYZ programmer - I am paid to accomplish a task. Perl adds value to many of my projects, even when they are not Perl projects. At my current job, I write AS3 in Flash. But our customers supply data in many forms, and Perl's ETL capabilities are necessary for turning the data into a form useable in our system.
One of the other posters broached the subject of whether you should learn a language just to get a certain job. That depends. Some popular languages are used by millions of programmers. When a company wants to hire a new staff member, they expect to find an experienced programmer who also is proficient in the language. To get such a job, you must already be experienced in the language as well as the industry. However, in newer languages (and out-of-date languages), there may be few programmers available who know the language and have a solid comp-sci background. Such was the case at my current place of employment. Rather than hire an ActionScript programmer, they chose to look for an experienced programmer who could learn ActionScript in a hurry. Prior to the interview they expected each candidate to study the language for a few days and write a program to solve a problem that they posed. I had never used ActionScript, but overcame that hurdle, learned the essentials in a weekend, wrote the program and got the job last Fall.