The former is wrong, the latter is correct. Simple as that :) There are cases where "si" is not mandatory though.
E.g. "Lei non ricorda nulla di me" (=She does not remember anything about me) is correct.
I don't know a scientific rule about that, but it seems allowed especially when "remember" can be translated by its literal (and literary!) italian counterpart, "rimembrare". Just like in Giacomo Leopardi's beautiful poem "A Silvia":
"Silvia, rimembri ancora
quel tempo della tua vita mortale,
quando beltà splendea
negli occhi tuoi ridenti e fuggitivi,
e tu, lieta e pensosa, il limitare
di gioventù salivi?"
"Silvia, do you recall
those days of mortal life,
when beauty sparkled in
your quick and gleaming eyes,
when, glad and pensive, the threshold
of youth you were to rise?"
It is not totally wrong, but it is more commemorative and should be used in sentences like "Ricordiamo le vittime dell'11 settembre" (=Let's commemorate the victims of 9/11)
"Remember" in a common acceptation is "ricordarsi [di]", reflexive, and needs preposition "di" .
In english, this example would be literally translated "She does not remember herself of me".
We could say "She herself does not remember me.", but that is as close to reflexive as English allows, since "remember" is not a reflexive verb.
Your literal translation does not exist in English. It is important to remember that prepositions often translate poorly from one language to another and we have to learn one expression to the other, just like "Look at" and "Look after" would be different in another language. We do say "Dream of", but "remember" takes the item or person remembered as a direct object and does not take any preposition nor reflexive pronoun. So we have to learn "remember (something or someone)" becomes "ricordarsi di (someone or something).
Yes, in English "remember" is not a reflexive verb, so "She herself" puts more emphasis on her and could be interpreted as: "She and no one else" or "Even she" or "she did not have someone else do it for her", but the sentence does remind me to put the reflexive pronoun into the Italian sentence. It is not a correct translation of the Italian.
Her secretary remembers me, but she herself does not remember me.
I have found on some forums that there's no difference in meaning between "ricordare" and "ricordarsi", so you can use the verb you like better. http://forums.about.com/discussions/Italian_Language/_/Dimenticare_vs_dimenticarsi/ab-italian/9689.1?nav=messages
And the preposition "di" goes with both "ricordare" and "ricordarsi". In Italian language there are certain verbs that are followed by one of the simple prepositions. http://italian.about.com/od/verbs/a/aa031908a.htm
Sorry, but "ricordare di" is wrong if the object is a noun. "Ricordare" is transitive and needs a direct object. "Di" is allowed only if the direct object is a subordinate sentence, to introduce it.
E.g. "Ricorda di santificare le feste".
"Ricordarsi" is intransitive (like all the reflexive verbs), and always needs "di" instead.
Finally, there are no significant differences in meaning (although "ricordarsi" deals more with day-by-day routine and "ricordare" is more commemorative) , but, depending on the context, one of them can be right or wrong.
"Non ricordo nulla", "Ricordami", "Oggi ricordiamo le vittime dell'attentato", "Ricorda le mie parole" - CORRECT
"Hai ricordato fare la spesa?", "Ricordo mai il suo compleanno" - WRONG
"Ricordati di me", "Ti sei ricordato di fare la spesa?", "Non mi ricordo mai del suo compleanno" - CORRECT
"Oggi ci ricordiamo delle vittime dell'attentato" - WRONG
it is needed, just like in English: She dresses herself beautifully. (herself is the reflexive pronoun) - so reflexive pronouns are used to express that an action is done to oneself. In Italian, the verb ricordare needs reflexive pronouns (in this sentence).
Conjugation would be like this:
io mi ricordo tu ti ricordi lui si ricorda noi ci ricordiamo voi vi ricordate loro si ricordano
"she" is 3rd person singular, and when you conjugate a verb in 3rd person singular it follows certain rules. The rules are; a) If a verb ends in a "y" and a vowel before that, it get a sufix "s"
example; I buy, you buy, he/she/it buys
b) If a verb ends in a "x" and a consonant before it, it ends in "ies"
example; I try, you try, he/she/it tries
c) If a verb ends in "ch", "sh", "ss", "x", "o", it gets sufix "es"
example; I do, you do, he/she/it does This is the case in the sentence "She does not remember me"
Hope this helps, good luck :) You can see more info here http://www.englishtenses.com/third_person_singular
Helping, or auxilary, verbs in English are tricky. The best thing to do is just memorize them: I don't We don't You don't You all don't He doesn't They don't
Another tricky verb choice is am/are. In your question you ask "what are the difference". Maybe this was a typo, but it is incorrect. There are two ways to say it correctly:
What is the difference? (Is and difference are both singular)
What are the differences? (Are and differences are both plural)
I hope this helps. :)
I've gathered that the verb in this sentence is actually recordarsi, not recordare, and the si detaches and moves in front of the verb in a sentence. It emphasizes the subject - she herself does not remember me.
The di must follow both reordarsi and recordare. Similar to how of always has to follow remind in English.