Yes, we celebrate holidays.
Because of DH's work schedule (he works rotating shifts & is sometimes scheduled to work on a holiday), we sometimes have to celebrate Christmas on a different day w/ our immediate family. Like, if he's scheduled to work on Christmas, we will have our special family Christmas day on whichever day off he has closest to Christmas. (We also do this w/ our birthdays if he's scheduled to work on a birthday.)
Both of our families live in our town, so both sets of grandparents normally have something at their houses on Easter, Fourth of July, & Thanksgiving, & Christmas Eve. Either I & the kids or DH (if he's not working), I, & the kids will split up those holidays between the 2 houses.
(As an aside, this past Fourth of July, older DS had a migraine, & we stayed home & did our own thing. It was SO NICE!!!)
We also visit both sets of grandparents on Mother's Day & Father's Day.
We do our own thing on New Year's Eve/New Year's Day, Valentine's Day, Memorial Day, Labor Day, & Halloween - sometimes, it involves the rest of the family & sometimes it doesn't.
Sometimes, because we do so much going back & forth between the 2 grandparents' houses, I feel like we're losing the "real meaning" behind the holidays... we're so rushed & stressed that I'm not really in any kind of holiday spirit. However, hopefully, we're making some good family memories for our kids, &, when they're grown, they'll remember all the visits to the grandparents' houses on holidays!