I was listening to one of Michael Thomas's Spanish tutorials and heard this sentence:
a veces se olvidan invitarme.
Why 'olvidarse' is used here instead of 'olvidar'? Is it wrong to just say:
a veces olvidan invitarme.
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Short answer: no, it's not wrong to say olvidar without se. There's a mistake in your first example, but it's not that. Keep reading.
There are a lot of answers to this question already in this site, but surprisingly it seems there's not one specifically about this one verb in this usage. Olvidar has a plain form and a so-called pronominal form (cited as olvidarse). Both mean the same, but they're not directly interchangeable. You would say
A veces olvidan invitarme. (plain form, verb + infinitive)
but if not you must say
A veces se olvidan de invitarme. (pronominal form, verb + de + infinitive)
A veces se les olvida invitarme. (double pronominal form, verb + infinitive)
That is, you can say
In (1) you simply use the verb as a plain transitive verb, the subject is the person who forgets and the direct object is the thing forgotten. In (2) it's the same, but the verb becomes pronominal (the reflexive pronoun is added); you can't use this with an infinitive as the object, though. In (3) the verb becomes intransitive but the thing forgotten is expressed as a complement with the preposition de. In (4) things become a bit more complicated: the person that forgets becomes the indirect object and the thing forgotten becomes the subject! This is a bit like what happens with gustar, but fortunately there's an exact parallel in English: when you say, for example, "Your meaning escapes me". There's also another parallel in Spanish: Se me ocurre (una idea), literally "An idea occurs to me".
The meaning of the four structures is exactly the same, but at least in my experience the pronominal forms are more informal and show more involvement of the subject. In my dialect (I'm from Argentina), no-one ever says olvidar algo; it's always olvidarse [de] algo, except in very formal contexts. I don't know about other regional dialects of Spanish.
P.S.: I've added a fourth pattern (olvidarse algo) for the sake of completeness, even though it's not applicable to this question because it cannot be used with infinitives.