"I like romantic movies."
Adjectives go before a noun (with 的) unless you are saying "NOUN is ADJECTIVE". So you could say:
是一部很浪漫的电影 (it's a very romantic film)
这部电影很浪漫 (this movie is romantic).
You will sometimes see it without the 的, but in general the most natural way is to leave the 的 there.