…Instead of the STL and similar
libraries in other languages?
Sometimes you want something that isn't in the library. I use circularly singly linked lists a lot. They aren't in the STL, they don't support STL sequences, and the implementation is so simple that rolling my own is simpler than downloading.
As a newbie, how much should I delve
into this part of software
development? Breadth first or depth?
Don't spend too much time. If you don't need it immediately, it's theoretical knowledge, and theory is useless without depth. Work through a good data structures book and skip whatever you find impossibly dull. If you know you'll be taking a data structures course later, pick up its book ahead of time.
(Although I tried just that and ended up with a useless book. Then I went to another school's bookstore, found a better book, and obtained proficiency credit without taking my school's course!)
Is only a conceptual understanding
necessary these days? Or should I be
able to implement a doubly linked list
blindfolded?
Take the middle ground. You need to know the properties of structures to be able to find bugs resulting from use of the wrong structure. But don't bore yourself implementing red-black trees, and certainly don't make a habit of coding structures you could get pre-made.