Traditionally, wedding gifts are given to a couple so that they can set up their new home together and prepare to raise a family. In modern times, however, many couples are older when they get married and do not need household items, while others pay for their own wedding and would prefer financial help over physical gifts. If you would prefer your guests to give cash as a wedding gift, you must go about making that request very carefully.
Many etiquette experts advise couples not to mention gifts or gift registries at all on their wedding invitations. This includes traditional gift registries as well as requests for monetary gifts. If you refrain from mentioning gifts on your invitation, be sure to tell your parents, your bridal party and other people that are very close to you that you would prefer money to physical gifts. Your guests will likely ask one of these people what you would like as a wedding gift and will be told of your preference.
If you want to buck tradition and simply state that you would like monetary gifts on your invitation, add the phrase "presentation preferred." This is a polite way of saying "we'd prefer cash as gifts." Alternately, you could add something like "In lieu of gifts, the bride and groom would appreciate donations towards their honeymoon," or something similar. This kind of phrasing is not appropriate for an overly formal invitation, but will work on a more casual style of invitation.
If you want to directly ask for money as gifts, you do not have to do so on the formal wedding invitation. Many couples now set up wedding websites that include details like directions to the wedding website and meal options that don't fit on the paper invitations. You can include a section on your wedding website explaining that you would prefer cash gifts. Simply include the URL of your site at the bottom of your paper invitation to direct guests to the website.
There are online services that allow couples to set up a registry to help them pay for portions of their honeymoon, a down payment on a home or just straight-up cash. This way guests don't have to hand you a check at the wedding, but can simply contribute to a lump sum. Again, it is considered gauche to mention the registry directly on your invitation, so either let those close to you spread the word or list the registry information on your wedding website.