After graduating from university is there a practical reason I would want to keep record of my previous assignments? I have a hard-drive full of them. Are there more practical reasons I don't see other than the sentimental value?
(1) You might have to prove to people that you took these classes. Transcripts may become unavailable or untrusted.
(2) Perhaps you'll find something of use for your own research or writing in them. Happened to me at least twice in graduate classes. (For example, a lemma I proved in homework turned out to be useful in a proof I wanted to write up elsewhere.) Of course, you probably will not want to reuse them verbatim (I cringe when I read my writing from 10 years ago), but they still can be better than nothing.
(3) You might eventually want to revisit one of the classes you have "casually" taken, for example because its subject is leaking into yours. By looking back on your homework, you'll get a quick impression of where you have left it (although this is only a good thing if you have been learning it reasonably thoroughly; if you were sloppy, then it might be better to start from scratch).
(4) In order to encourage your own students to submit LaTeXed assignments, you will want to provide a usable blank LaTeX template for them. And where do you get such a thing? (Well, there are several places, but one is in your own homework folder.)