SICP -- K&R -- CLR[1] -- Design Patterns -- Mythical Mammoth -- TAOCP -- Compilers (Dragon Book) -- Effective C++[2] -- Programming Pearls -- Peopleware -- Little Schemer[3] -- Modern C++ Design -- The Practice of Programming[4]
[1] ... except I'd recommend Skiena instead of CLR.
[2] ... except I'd recommend Effective STL over any other Meyer book, and I also wouldn't concede that C++ is essential.
[3] ... except I'd recommend Lisp In Small Pieces, which I know is a totally different book, but do you need it and SICP?
[4] ... but only to someone new to programming.
You can see I've chucked all the methodology and career crap (except for Brooks and Peopleware; I think you probably already know everything in Brooks, but Peopleware is something you should reread annually).
To that list I might add:
On Lisp -- Javascript: The Good Parts -- Pattern Oriented Software Design #2[1] -- Computation Structures -- Computer Architecture (Hennesy and Patterson) -- C Interfaces and Implementations -- The Visual Display Of Quantitative Information -- Windows Internals[2]
[1] ... this book was wildly* ahead of its time and is no doubt overlooked because of it's patterns-y enterprise-y marketing.*
[2] ... 10 years ago I'd have recommended _The Magic Garden_ but, even though I'd rather eat a bug than use a WinAPI system full time, it's hard for me to argue that Unix kernel design is as relevant now as the Windows kernel --- and, more importantly, there's no Unix book that does as good a job as Russinovich on the Intel architecture.
I wish I had good books to recommend on:
SQL performance optimization -- distributed systems -- compression and coding -- the HTML/JS DOM programming model.
The reality is, at this point in my career, I don't find myself going to books for programming stuff so much; that doesn't mean I don't read, but I tend to take the "man pages" approach. So my choices may date me. If I'm going to pick up a book today, it's going to be for something domain specific. I find myself reading for maths (I suck at math), or for graphics, or for market microstructure, or signal processing. I won't pretend that stuff is relevant for everyone. I feel confident, though, in saying that nobody needs more than one "Agile" book.