It's not uncommon to bring wedding gifts to a wedding. The couple will probably arrange for a gift table to be set up at the reception. You may also find a white birdcage on the table for guests to slip cash or checks in envelopes into.
Cash and checks are not heavy and easy to carry but boxes of wedding gifts are a little more difficult to leave a wedding reception with.
As the bride and groom you should decided before the wedding wedding who will be in charge of taking the wedding gifts at the end of the night and where they are going to put them.
If the bride and groom are returning home after the wedding then make sure there is enough room in the car for gift bags and boxes. If the newlyweds are heading to a hotel or leaving right aways for their honeymoon then a friend or family member should be put in charge of making sure all the gifts are taken from the reception and brought to either the couple's home or someone else's home.
As a wedding guest you can help the bride and groom out by shipping your gifts to their home before the wedding. Don't have it arrive while they're on their honeymoon because there won't be anyone to accept it.