So far mostly the material from those books has been available to me in the code written by others, some of the famous open source code and in Microsoft's .NET.
There is a case where I exploited the heap data structure (that is, as in heap sort) to create an efficient priority queue, and I didn't find code for that ready to use by others.
There is a case where I might take k-D trees (finite dimensional trees for essentially a multi-dimensional version of binary search) and modify it to get an algorithm I might need, but so far I haven't.
Generally we have to expect that what was in D. Knuth's TACP in the 1960s and commonly useful now has been put into libraries for use by others.
This is a common situation: For the simplex algorithm for optimization, rarely would it be advisable to try to code up a version yourself. Instead get a copy of C-PLEX, the IBM OSL (Optimization Subroutine Library) or some other respected code. Then knowing how simplex works would be helpful, but not because want to code the algorithm from scratch yourself.
The core of my work is some new work in algorithms, but those algorithms would not be good candidates for a library for general use. So, yes, I work with algorithms occasionally but mostly don't code the ones in the college texts.
However, is it useful to know that such and such data structure is more efficient than that other structure over there for what I want to do with it? Yes. Is it important to be able to think in terms of other algorithms you've learned that might make what you're working on easier and more efficient? Absolutely.
I have never once implemented any of the algorithms or data structures that we learned about in my intro to algorithms/data structures class, other than for the class itself. But learning how those algorithms and data structures work, even if I can't remember the specifics of all of them at the top of my head, has has helped me to be a much more efficient programmer because they gave me the tools to think as such.
So, do you need to know specifics about exactly how every algorithm or data structure works, probably not unless that specifically is your job. But is it useful to have a basic understanding? Absolutely.
Storing and organizing data. There you go. If you write code, you are always storing/organizing/manipulating data aren't you. whether it is front end, back end whatever. Everything is data end of the day.
Now I am of course not saying that you must know linked list or stacks or queques etc. But you must know data structures in general because that is a core foundation. [1] http://en.wikipedia.org/wiki/Data_structure