In the US it is never appropriate according to wedding etiquette to ask for a wedding gift. Wedding couples assume they will probably receive gifts, and as such they tend to register to give well-wishers suggestions on their wants or needs. Certainly money makes a nice wedding gift, but it is one that cannot be applied for under most circumstances.
There are a few exceptions. A couple might ask for financial help in paying for a wedding from either the bride or groom’s parents. Usually this help is offered, or there is an assumption that it will be offered. Traditionally the bride’s family funds the wedding and reception, while the groom’s family pays for the rehearsal dinner. The couple should not expect an additional wedding gift from parents paying for a wedding.
What tends to annoy those who specialize in wedding etiquette is that some couples request specifically for a wedding gift to finance a honeymoon, or to pay for a home repair project. Such a request for a cash wedding gift, particularly in an invitation is considered quite rude, and is liable to offend most people attending.
Etiquette experts recommend instead that one budget a wedding accordingly, and give it funding that will allow one to also take a honeymoon, or use needed funds for projects. By careful budgeting, amount spent can be reduced and thus one can provide guests with a nice wedding, while not being accused of throwing a wedding for the sake of receiving a cash wedding gift.
Another exception may exist in the cultural tradition known as the bridal purse. This is a typical European tradition, and is still observed when most guests understand the tradition. In such, the bride carries a silk purse, and may circle round the guests. Willing guests give the bride checks or cash to fill the purse.
When this tradition is observed, the bride and groom do not usually register for other gifts. However, this tradition should really only be practiced when one can be assured that guests will not be offended by it or consider it as asking for a handout. It is okay for a few friends not to know about the tradition, and their failure to provide a cash wedding gift should not be viewed as insulting. It is poor etiquette to inform friends of the tradition in advance unless one is asked.
Thus, if a bridal purse is part of one’s cultural tradition, the invitation should still not include a request for a cash wedding gift. Instead, it is assumed that people attending the wedding will be aware of the tradition and not come empty-handed.