Quick answer
parecer = to seem, to look like, or to be someone’s opinion (me parece que…).
parecerse a = to resemble, to look like someone else.
Resemblance between two people or things always needs the reflexive pronoun plus a.
Side by side
Parece mi hermano. / Se parece a mi hermano.The first says he seems to be my brother; the second says he resembles him.
¿Qué te parece?What do you think? — the standard way of asking for an opinion.
Nos parecemos en el carácter.We are alike in character — parecerse can take en for the respect in which you are alike.
Memory trick
Comparing two people needs both pieces: the pronoun and <b>a</b>. Anything about impressions or opinions drops both.
Typical mistakes
Parezco a mi madre.
Me parezco a mi madre.
Resemblance needs the reflexive pronoun. Without it the sentence reads as "I seem to my mother".
Me parece a que va a llover.
Me parece que va a llover.
The opinion structure is me parece que, with no a. The a belongs only to parecerse.
Check yourself
Fill in: "Mi hijo ___ mucho a su abuelo."