As from 1-1-2018 new regulations will be in place for scooters and mopeds in Amsterdam. Scooters and mopeds from before 2010 are no longer welcome in most of the city (exception is the rural area of Amsterdam North; the Durgerdam, Holysloot, Ransdorp and Zunderdorp villages). Although there are some exceptions, almost all ‘old’ scooters and mopeds will be banned.
If you would like to buy a scooter or a moped please do take note of its production date; buying a cheap one from before 2010 may turn out to be an expensive decision in the end.
Moreover, the community of Amsterdam aims to ban scooters and mopeds from bike paths. They would have to use the main road (between cars/buses, this is also quite risky). Reason is that the bike paths are very crowded already without the scooters and mopeds and that they are involved in a very high number of accidents. 80% of all scooter riders regularly exceed their speeding limit, making bikers feel unsafe. New national legislation will be needed to implement this regulation. The earliest start date can be March 2018. Amsterdam is ambitious and aims for the soonest implementation date possible.
It may well be possible that other big cities (the Hague, Rotterdam, Utrecht, Eindhoven) will follow the example that Amsterdam has set.
Please see https://www.iamsterdam.com/en/living/latest-news/new-rules-for-scooters-and-mopeds for more information.