Dowry is practiced by many cultures, ethnics and religions.. some cultures require women to give dowry and others vice versa.. I believe many topics have discussed on this however, why women deserve the 'previlege' more thn men..?
In Hindu
Dowry (Dahej/Hunda) as we all know is paid in cash or kind by the bride's family to the groom' s family alongwith the giving away of the bride (Kanya-dana). The ritual of Kanya-dana is an essential aspect in Hindu marital rites: Kanya = daughter, dana = gift. A reason for the origin of dowry could perhaps be that the groom and his family had to take up the 'onerous' responsibility of supporting the bride for the rest of her life.
Bride-price on the other hand involves the receipt of presents, in cash or kind, by the bride's family in return for giving away of the bride. Hence bride-price has the character of an exchange.
source: http://www.hindubooks.org/sudheer_birodkar/hindu_history/practices1.html
In Chinese Society
Several days after the presentation of the betrothal gifts, the girls family sent porters with an inventoried dowry to the boys house. The dowry consisted of practical items, including a chamber pot, filled for the occasion with fruit and strings of coins. This procession gave the girls family the opportunity to display both their social status and their love for their daughter, and wealthy parents often included serving girls to attend their daughter in her new home.
source http://www.chcp.org/wedding.html