There is no concept of dowry in Islam from the bride's side. The amount of mahr (marriage gift paid to the bride) must be according to the ability of the groom.
Islam recognizes customs as far as the amount of mahr is considered, but it has to be within the Islamic guidelines. It is true that there is no limit for mahr, but when it becomes a burden, then it is not encouraged by Islam.
At the same time, dowry (jahaiz-a gift of the bride's parents to the bride) may also be accepted if it is voluntarily done. However, it cannot be demanded for just like mahr.