I managed to keep three generations of cats off the table, but the current kittens are incorrigible – and maybe I’m mellowing.
Something like the link below but much prettier. It is a tree with glass votives on it. Mine is more round like a tree. I either put tea candles or fill them with water and put single stem flowers in them. I had purchased it from a store called “Illuminations” which was a very nice decorative candle store.
https://www.amazon.com/Kennedys-Country-Collection-71457-Candelabra/dp/B00EEFQC0E/ref=sr_1_fkmr0_4?s=furniture&ie=UTF8&qid=1519264426&sr=1-4-fkmr0&keywords=tree+votive+candelabra
We don’t have a kitchen table and haven’t for years. We have a very large island and eat most meals there as it’s just DH and me. No placemats or centerpiece on the island. However, we have a large, rustic trestle table in the big room in the center of our house that we use when we entertain, and that is set up with a runner and two iron candelabra with an antique dough trough in between that I fill with flowers, fruit, or seasonal decor.
Our kitchen table is an extended rectangle that used to seat 5 in a very small kitchen not meant for a table. Now it seats two empty nesters, a basket of paper napkins, and a pile of newspaper sections that gets moved once a week or so to DH’s pile on the dining room sideboard where they will live until the next time company who he wants to impress comes to visit. (That hasn’t happened in almost 20 years…but knowing which battles to fight has made our partnership last this long, on both sides.) At dinner, I move S&P and a spice or two to the table. We do use placements - plastic when the kids were small but now primarily cloth and some British pub mats; these cycle by meal and season.
The dining room table occasionally has a vase of fresh flowers in the center, especially in the summer when we bring in flowers from the garden. We only use it for dining once a week for Shabbat dinner, and otherwise it serves as a handy spot for my work papers.
Oh dear, we’re supposed to have a centerpiece? 
I like to have something colorful or decorative, but since we serve all our meals family style, having a centerpiece just interferes with the placement of food. So I use colorful and seasonal table cloths. I always look for clearance items after a holiday so I don’t pay much for them. I mostly use vinyl ones so we can wipe them off. Right now the Valentine’s Day one is on, but it will soon be replaced by the new St. Patrick’s Day one I picked up last year. Then the Easter one will go on. I have American flag theme, fall leaves, Halloween, Christmas, and one we put out just for birthdays. And two “regular” ones that I use during non holiday times.
I never buy decorative items that are not functional… but I love to decorate with functional items. I have a set of beautiful leather placemats I brought from Chile, which replaced an older set of beautiful leather placemats I brought from Argentina. I have a nice bronze tray with salt and pepper shakers, napkins, and several decorative crystal and metal bowls, most from Michael Aram collection, that hold dried fruit, nuts and honey. Sometimes I also add a very small vase with fresh flowers or greens. The tray can be easily moved out of the way if we need more space.
I have a small kitchen, so no kitchen table or island. The dining room table always has placemats on it and a tile/trivet in the center that DH and I bought on Catalina Island on our honeymoon. There are always salt and pepper shakers and sometimes fresh flowers on it also. I used to keep the table pretty clear when the kids were young, but now that one has moved away and the other is in college, one end of it generally has a lot of stuff on it that I only clear away when friends come over to play mahjong or when the kids are home.
Usually round woven colorful placemats on the table with a round wrought iron and glass tray centerpiece that holds salt/pepper shakers and a napkin holder. In summer, I add a small vase with flowers from the backyard. The dining room table has a large vase with flowers from Pier One that I fell in love with several years ago. It used to be an internet cafe when the kids were home, laptops at half the seats. The island has a pottery pedestal fruit bowl filled with fruit.
Most of you have bare wood or glass with placemats? Sounds nice. I have table cloths, even on my two person kitchen table, pushed up against the window. Usually there are flowers, and if nothing fresh, then the dried statice in a vase. My dining room has candles in various sizes, flowers in summer, and all the trivets, some made by my daughter. What I don’t want to mention is the collection of mail and paperwork that gets moved for guests.
Our tables are all granite top. When we moved. the round tabletop was easy - we just rolled it and then lifted onto the base. The large rectangular top required “hired help” - our young triathlete friend was happy to help. He was well fed at said table post-assembly. We use plastic or fabric placemats when we eat. We also have a firetable on the deck to eat in the summer. That table is aluminum, and the fire is the centerpiece. 
Again, placemats, no tablecloths. I can’t remember when it was the last time we used one… I gave them away with the ugly oak table with clawfeet leg (yuck!) that served as our dining table in the beginning of our married life.
Junk mail and unopened bills 
@veruca, I like your style.
No centerpiece. As @doschicos - mine is completely bare. Well, not right now, as all the tax prep stuff is on it.
I keep the woven placemats on the kitchen table along with the current week’s NYTIMES. We keep the wooden dining room table bare. If just DH and for dinner and we are in the dining room, use placements. If having company, we generally use table cloths in the dining room. Kitchen table also has a wooden napkin holder. Use that table for breakfast and dinner during the week, not generally on the weekend if dining at home. Not home for lunch except on the weekend. Once the weather turns warm enough we have dinner on our deck outside every night and frequently for breakfast as well.
This thread just reminded me of the vinyl placemats the daughter’s used when they were little for the kitchen table that I haven’t thought about in years… .first Sesame Street, then alphabets, US map, solar system, ballet poses and so on and so on.
I still have the US map placemat in my kitchen cabinet.
We have placemats that have translations of phrases from English to that language. The choices of phrases is very weird. According to my son’s girl friend from Hong Kong - the Chinese place mat - is mostly Mandarin, but uses weird combinations of transliteration systems.
I haven’t starting looking yet for what I’m putting in the middle. I got rid of the basket with flowers and greenery. I’d like something low that just brings color and I don’t have to move. I’ll find it. Would love new placemats too.
Re: maps – we used to have a 4x6 foot US map in our dining room! Good memories. We used it to plan national park trips with it, show where our far-flung family lives, etc. .