Madeira - how about taxis ?

Sorry but you are wrong. Madeira has very good bus services that cover most of the island, check out http://www.sam.pt/ and http://www.rodoeste.pt/Index1.html but there will always be gaps.
The places you will not get a bus to are Pico do Arieiro and Achada do Teixeira, you need a taxi or guided walking tour. Also as far as I know Queimadas is not on a bus route.
To get to the Lombo do Mouro walk you need to get a bus up to Encumeada junction and the walk up the main road then its all downhill from there.
For walking the best guide is http://www.sunflowerbooks.co.uk/madeira.htm which also has bus timetables.
Taxis are plentiful all over but day hires are not cheap! There are plenty other good walks on the bus routes.

Thank you d_edinburgh for your information and for the links to the websites.

I had already bought and read the Sunflower guide and studied the bus timetables in it.
That's how I came to the conclusion that bus services on Madeira are very limited.
Now I can understand that public transport is initially for the habitants and thus doesn't go to places only interesting for tourists, like starting points for walks.
But even between the different towns the connections are limited. Perhaps you will consider me a 'spoiled tourist'.

When I search in the timetables for busses going from Funchal to Santana for instance, I find # 103 leaving Funchal at 7.30 am arriving in Santana at 9.15 am. The latest bus going back to Funchal leaves Santana at 5.30 pm. I don't think this leaves enough time to visit Santana, to take a taxi to Achada do Teixeira or to Queimadas and to make one of the walks (even forgetting lunch).

The problem is that I was advised to choose Funchal as the place to stay throughout my vacation. From there I would be able to go to about everywhere on Madeira and return the same day.
I realise now that was a bad advice. It takes already one hour to one hour and a half to reach Ribeira Brava from Funchal. I don't know if this is because of the traffic, the bad road or the many stops on the way ...

To visit the western part of the island I guess that Ribeira Brava is a better place to be based.
Anyway now I'm looking for other places on the island to stay for the night. Funchal as the place for all overnights doesn't seem to be such a good idea.

Too bad no readers of TT have information about taxi fares.

But again thank you for your help d_edinburgh.