Wedding table centerpieces are most commonly thought of as flower arrangements. You can go with bouquets using the same type of flowers as the ones in the bride's bouquet or you can pick one or two of the flowers of the bride and use that as a subtle but elegant accent in your dining room. You can also play with the flowers in different ways here by maybe using longer stems if you want to 'lift' the arrangement up a bit.
Consider the height of the flowers and the vase they are in; if they are low or a little higher than eye height people can still look at each other across the table, but a height in between may cut off people from each other. The vase will obviously contribute to the height of the table centerpiece so keep that in mind. Talk to your florist about what would work best. Also, do ask your florist if they loan out vases or if you will need to get them yourself. If you need to get them yourself, there are many stores that will sell vases that work well for occasions like a wedding.
If you are going with flowers it is great to consider this when you order the rest of your flowers from your florist.
Now if you want to look for something other than flowers there are lots of alternatives; let the surroundings, the season and your personality allow you to explore your options. Some things that can be done are for example to use balloons (anchored by a weight on the table), another idea is to use candles (this gives a nice effect to the light in the room and also creates a cozy feeling during the chiller seasons). Arrangements with water – either having candles floating or maybe flowers can also be used. Again, lots of options, so keep your eyes open and when you least expect it something can inspire you.