For Amsterdam there are basically three different discount cards available. All of them save you waiting time for buying tickets (you may still have to join a line for getting in)
1. I Amsterdam Card
This card is issued by the Amsterdam Tourist board. It includes entrance to most museums in Amsterdam (but not Anne Frank house and for the Rijksmuseum you just get a E 2.50 discount).
It also includes public transport within Amsterdam and a canal cruise.
You can buy cards that are valid for 1 or a few days.
2. Holland Pass
The Holland Pass works with 'Golden' and 'Silver' tickets, that can save you quite a bit of money, especially if spent smartly.
It has attractions/museums not only in Amsterdam, but also in interesting towns nearby.
It includes a single train ticket from Schiphol Airport to Amsterdam and a canal cruise.
The pass is valid for a month.
This card has not been developed for tourists, but rather for the locals - but anybody can buy it anyway.
This card only includes access to museums, all over the Netherlands. So, attractions are not included and neither is public transport, or excursions or a canal cruise. It is the only card that also includes the Anne Frank House.
The cards is valid for a year.
Iamsterdam City Card