It turns out I'm incorrect, I was looking it up to check something. It was the Great Giana Sisters, featuring Giana and her sister Maria (my favourite, I think she wore a better colour). But even so, I never played Super Mario at that time, so I don't know. There was a lot of hitting blocks for power-ups and jumping on monsters, so probably. Check it out (http://www.youtube.com/watch?v=YMTdr026bZU).

It's funny, I still sort of really remember that music, even all these years later.