Se me olvida, I forgot!

Se me ha olvidado quién soy yo

I have forgotten who I am

Caption 2, Cienfue - Medio Alcohólico Melancólico
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As English speakers, we might be wondering why “I have forgotten,” in the caption above, isn’t using the first person (yo or "I") conjugation of haber, as in [yo] he olvidado...

In fact, Cienfue could have sung precisely that, which would be the most “English-like” way of expressing his thought:

[yo] he olvidado quién soy yo
I have forgotten who I am

Another alternative would be the pronominal (think “reflexive”) form, olvidarse:

[yo] me he olvidado de quién soy yo
I have forgotten who I am

Note that the pronominal option requires a “de” after olvidado. The reason for this is that olvidarse, like most pronominal verbs, does not take a direct object, while olvidar is “transitive”—meaning it does (and must) take a direct object. Native speakers often just “know” this instinctively.

Cienfue doesn’t opt for either of these, rather going with what, to English speakers, will be the most “foreign” (though commonplace in Spanish) construction, olvidársele. Olvidársele is what is known as the "impersonal" (or “terciopersonal,” third person) construction of olvidarse.

In contrast to what we are accustomed to in English, the subject of the sentence is the thing forgotten, while the person doing the forgetting is expressed as an indirect object (signified by the le appended to olvidarse). Something "gets forgotten" (passive voice) "by someone."

So, when Cienfue sings,

Se me ha olvidado quién soy yo

the subject of the sentence is “quién soy yo” (who I am) and the indirect object is “me” (me).

Cienfue is most literally saying:
“ ‘Who I am’ has been forgotten by me”

Most Spanish speakers, even if pressed, will find precious little (if any) difference in meaning amongst the three possible constructions. There are definitely regional as well as personal preferences.

It can also be argued that there are nuanced differences in emphasis. For example, the “impersonal” form places the least “blame” on the person doing the forgetting. This type of verb construction has even been called sin culpa (without blame), and it’s not the first time we’ve encountered it in our discussions.

What if you want to simply say "I forgot."? (e.g. in response to Por qué no fuiste a trabajar? Why didn't you go to work?)

Olvidé. INCORRECT (requires a direct object.)
Lo olvidé. (I forgot.) (direct object pronoun lo refers to “work”)
Me olvidé. (I forgot)
Se me olvidó. (I forgot.)

Let's cap this off with a few more examples of each possible olvidar constructions: transitive (the most "English-like", and perhaps least common), pronominal (looks like "reflexive") and impersonal:

You forget that I am the boss?
¿Olvidas que yo soy el jefe?
¿Te olvidas de que yo soy el jefe?
¿Se te olvida que yo soy el jefe?

Maria forgot to pick up her cat.
Maria olvidó recoger su gato.
Maria se olvidó de recoger su gato.
A Maria se le olvidó recoger su gato.

Jorge forgot his money.
Jorge olvidó el dinero.
Jorge se olvidó del dinero.

[In some cases, like this one, the pronominal form alters the meaning slightly. “Jorge forgot about the money,” or even “Jorge kissed the money goodbye.”]

A Jorge se le olvidó el dinero.

Now is a good time to catch up on (or review) these related lessons:

Accidental Grammar
Caer Bien: To Like It
Gustar: To Like, to Please, to Taste
“Le” in Verbs Like Gusta