The problem with any book list like this is the scope. Software is turning into a very diverse culture, a very heterogeneous ecosystem. Subjects that are very important to one area might not be as important to other areas. Design patterns are essential for enterprise development, not so much for AI and low level systems programming. Algorithms are essential for the latest but not for the former.

Given this, there are some books you might add or remove depending on the area you are interested (e.g.: Knuth's "Art of Computer Programming", Martin Fowler's "Patterns of Enterprise Application Architecture", ...)

To finish, 2 books people recommend a lot for beginning programmers:

"The Pragmatic Programmer"- Hunt, Thomas: a very good book, with sound advice and very easy to read. The only bad side is that it became so influential that its ideas became vulgarized in thousands of blogs.

"Code Complete" - Steve McConnel : A very dangerous book. It does give have a lot of sound advice. But, IMO, it has some big problems. First is that it gives the false impression that there is a lot of empirical evidence on what works on software engineering. Second, it perpetuates some myths that don't have such evidence: the "orders of magnitude programmer's productivity" and "the cone of uncertainty" (see: https://leanpub.com/leprechauns).