I don't think it is weird. It is usual.

You can think about it like about the verb "to please" in English.

Огурец мне нравится. - The cucumber pleases me. Cucumber is a subject, me is an object.

As soon as word order in Russian is more free than in English (due to the case system) "Мне нравится огурец" is almost the same as "Огурец нравится мне".

BTW Spanish verb "gustar" works exactly like that.