When to learn category theory?

Luckily these days there is a beautiful text that teaches algebra and category theory at the same time: Aluffi - Chapter 0. It deserves to be more well-known. Besides the fact that it uses (basic) category language from the outset, it is very well-written. If I would ever teach an algebra course, this would probably the text I would use.

I very often find some knowledge of category theory useful to understand things conceptually.

A book that one could read before studying mathematics at the university is Lawvere's and Schanuel's Conceptual mathematics. This is an introduction to category theoretic ideas on a most elementary level.

Edit: two days ago, there appeared a very interesting-looking book by David I. Spivak on the arxiv called Category theory for scientists.