• Learning Perl -- A great starting point.
• Intermediate Perl -- Teaches you about references, packages, objects, and an intro to testing.
• Programming Perl -- Great detail on the language, and one of the best treatments on Unicode I've seen.
• Advanced Perl Programming -- Older book, but learn far more than everything you ever wanted to know about typeglobs, as well as intro to parsing, using templates, a brief tutorial on Perl XS and Inline::C.
• Perl Cookbook -- Older book, but much of it is still relevant. It's helpful in learning idiomatic Perl, and "get the job done" Perl, though some of the idioms may have been superseded by now.
• Modern Perl -- Learn how people are using Perl in the 21st Century. Intro to Moose, more on testing, modern good practices and idioms.
• Higher Order Perl -- Never fear wielding callbacks and coderefs again. Learn how to apply functional techniques to Perl.
• Mastering Regular Expressions -- Older book, but there's still no better resource for learning regexes inside and out.
• Perl Best Practices -- Ok, so some of them fizzled, and some were controversial, but if you learn anything from this book, learn to think in terms of best practices (not necessarily to blindly follow the ones asserted in the book).
• Mastering Perl -- Rounds out the Learning, Intermediate , Mastering series. Good read.
• Programming the Perl DBI -- Older book, but IMHO, before you can hope to make good use of DBIx::Class, you should understand how DBI works, and this book will get you there.
• Mastering Algorithms with Perl -- Older book, and some of it is not modern-day idiomatic Perl. But algorithms themselves don't change much over the years, and I still refer back to it from time to time. It was one of the most approachable algorithms books I ever read.
• Perl Testing: A Developer's Notebook -- If you aren't writing tests, there's more to learn. :)

This is an incomplete list. There are also the specialization books; a book on LWP, a book on XML, a book on using TT2, a book on CGI (CGI is becoming irrelevant, but understanding the mechanics of a stateless ecosystem is still good knowledge, as it's still applicable in web development). There's a good network programming book too.

There's an Apress book by Sam Treagar on writing modules for CPAN.

And then there are the books that aren't Perl-related, but that approach topics that Perl can be applied to. My personal opinion is there's never a shortage of topics to read up on. ;)