Mark W said:
"Me comí una hamburguesa" vs. "Comí una hamburguesa". Both are grammatically correct.
Grammatically correct, maybe, but who says "¿Has comido ya la manzana'". Most people, almost all the time, would say "¿Te has comido ya la manzana'", and they'd probably look puzzled if you omitted the "te". This dative could possible be omitted sometimes, but it has its uses too: it indicates that a specific amount of food has been consumed; without it you assume it is unspecific.
Regarding the "me" with "creer", again, its presence is not just for mere emphasis: used with "creer" it can indicate that someone acts as if he is important, knows everything, and with disregards to others, used often by people to indicate someone's arrogance, like in "Se cree que lo sabe todo". It is also used to indicate that someone believes something without questioning it, or in an innocent way: "¡Se lo ha creído!". The nuances added by the "se" to "creer" are no different than those you obtain with many prepositions in phrasal verbs. For example, in "¿Qué te has creído'", you cannot omit "te", or you'd modify the meaning of the sentence.