Yes, I send thank you cards or notes for gifts most of the time. I don’t send thank you’s to my mom or dad, because they never had me write them when I was a kid. I think if it was important to them, I’d have written at least one thank you before my wedding shower.
With three kids, I end up sending a lot of cards. After each birthday and Christmas, the cards go out. My daughter is old enough to write her own, and the boys sign their names to cards I write. I think my 6 year old will write his own cards after his upcoming 7th birthday. They’ll be short, but sweet! My husband’s family is more traditional than mine, and they place a lot of importance on thank you cards. I always make sure not to leave any of them out, and my grandma always gets a handwritten thank you. I only use Facebook or email to thank people for something that wasn’t actually a gift. For example, yesterday my sister-in-law took my two boys hiking and fed them dinner at her house. She got a thanks on her FB page. :)