When does one write an accent on demonstratives 'demonstrativos' (éste, ése, aquél)?

What is the difference between the demostrativos with an accent and without an accent? When do I use the one with the accent?

Good Question. Many Spanish speakers probably do not know the correct answer.

Before 1959, the Royal Spanish Academy required an accent be put on demonstrative pronouns, i.e. 'this one' 'that one:'

¿ése libro? No, aquél.	That book? No, that one (over there).
éste es tuyo.	This book is yours.

In 1959, the Royal Spanish Academy changed rule, decreeing that an accent was only necessary in ambiguous cases. For example, ése compra 'that woman buying' and ese compra 'that purchase.'

However, many major publications such as the Spanish dailies El Mundo and El País stick to the old rule.

So, to answer your question, I guess it depends on who you place more confidence in--the Royal Spanish Academy or major Spanish publications.