Encumeada. Don't miss this one! Way up in the mountains (easy to reach by car) there is a wall where the clouds run down the slope like a waterfall. If you're there at the right time (which is fairly often) you're in for an amazing experience. It is a bit of a gamble since you never know when, but try it out!
Pico do Arieiro.With it's 1819 metres, Arieiro is the second highest mountaintop on Madeira. It can be reached by car, and from here you can walk (a long and scary walk) to the highest one, Pico Ruivo (1834 m). I didn't go there. Of course it wasn't because of fear, I just didn't feel like it ;) Too much trouble for fifteen measly metres! The Pico do Arieiro is amazing. There are two miradouras, or viewpoints, from where you can see almost the whole island!
When we had lunch on the north viewpoint, we were attacked by really friendly and hungry lizards! They crawled all over us and ate the crumbs of our sandwiches (they were also fond of my nail polish and tried to bite my finger off. Luckily they had no teeth..) I later learned that this was the Madeira Lizard, an endemic species. Very cute.
Madeira is a Mecca for trekkers, since it has irrigation channels, "levadas" all over. Not only do they provide water, but very beautiful walks thanks to concrete maintenance paths. The levadas go high up in the mountains, in the countryside and even downtown!
This is a levada we walked, Waterfall Risque. Amazing views! Try it!