I like that idea! One thing you could do is put together a bunch of trivia questions about you and your fiance (such as, "how many dresses did the bride try on before finding THE dress?" or "how many baseball stadiums have we visited together throughout our relationship?"), allow people time during cocktail hour or dinner to fill them out, announce the correct answers after dinner, and give the centerpieces to those who got the most correct (or, whoever got the most correct at each table would get to take the centerpiece from their table).
My SIL did this at her wedding and I will be doing it at mine also. I will have enough for each couple so I wont have to choose but she picked who she wanted to have the centerpieces before the wedding and put a note under their plate saying they were to take it home. I've also heard that if people are sitting at assigned tables but randome seats, you can put something randomly under one plate at each table and whoever sits in that seat, gets it. The trivia idea is cute too!
My mom tells me I should tape a penny to the bottom of a chair at each table and then whoever sits there gets to take it home. She keeps telling me people will fight over them lol. I could care less honestly.
I attended a wedding a couple years ago where they did some sort of game to give them away. I can't remember what it was, but it was something fun. I ended up winning, actually! It was a lantern with a candle on top of a wood block and a small vase with faux flowers inside. Good way to help the decor not go to waste!
Daughter and I talked about who she wanted to offer them to and then I sent an email a couple days before the wedding and invited them to take one at the end of the reception. We focused on people who live locally (no one flying was going to want to take a floral arrangement). Four of her five BMs live long distance, but all their moms/families still live local to the wedding location, so she encouraged them to each take one home for their mom. So, we ended up offering them to a few aunts and close family friends, and the BMs to take home to their moms. There were a couple extras that we brought home, and the next day FOB delivered them to a few of our older neighbors (who weren't invited to the wedding, but knew about it).
My cousin gave away her center pieces but she didn't do anything to have people win them or anything. She just made an announcement if people wanted to take them they could. Luckily they weren't something everyone would want so nobody fought over them. However with my wedding it's very diy and so because of that we need a lot of people helping us set up and take down. Since we will have people helping with the wedding they get the center pieces. Our center pieces are these big bottles with lights.