If you're getting a bike for as little as 20 EUR, except it to be stolen, if it is not obviously a "frankenbike" made from spare parts of discarded half-bikes. I have no respect for people that buy stolen bikes (yet many people do).
The bikes I've owned (they do get stolen a lot ...) were usually about 100-150 EUR for a sturdy no-frills "grandma bike". I might be able to get one cheaper second-hand if I looked harder, but when I'm without a bike, I really do need a new one quickly because it's my main means of getting around in the city, cars are inefficient (in the city) and public transport quickly adds up the costs you might as well have spent on that new (or second-hand) bike.
Amsterdam might not be a good example though, I've heard from my friends that live there it's annoying to get around in the touristic city centre, because of the tourists. Not even so much because the foreign tourists aren't used to bikes, but (from my own experience) tourists generally walk around in groups and Amsterdam's sidewalks are small, so they just sort of spill everywhere.
BTW I have never seen a "cars are guests" sign, anyone know what cities have those?
Here's a funny video of an American tourist reacting to the car-free city centre of Groningen: http://www.youtube.com/watch?v=x7gi2RxM1Qg (I'm aware it's not really representative of the typical American tourist, don't worry, but it's quite amusing still :) also for accuracy: the centre is not completely car-free; taxis, buses, police, ambulances etc are allowed, and there's a sort of maze of one-way streets that cars can take if they really need to be somewhere, except for the roads directly next to the very central city square)