No. Household rates cover refuse collection. Water and sewerage are separate. Medical care - except dentistry - is free at point of delivery except for prescriptions and that depends on your status - or so I understand it after not living there for a while.
In Belgium we also pay every time we visit a doctor but it's refunded wholly or in part by the Mutuelle insurance depending on problem and patient status - which concentrates the mind about not bothering GPS for colds and other minor ailments that can bet treated with advice from the pharmacy or even common sense.
Some prescriptions, eg cancer drugs, are refunded 100%. Others such as contraceptives are not funded at all. Children's meds are funded differently too. Medicines can only be bought from a pharmacy, unlike in the UK where you can get some at the supermarket or off the shelf in a drugstore. I like the Belgian system. It's rapid, efficient, effective and hard to abuse.