Mine is closed off, but my laundry is in there and I wanted to be able to hide messes/noise.

Same here. Thought it might also help keep some of the dust and dirt confined in there. We also keep the dog in the sometimes.

Do you have anyone or anything that you want to keep out of or in there, such as toddlers, pets, in-laws? Might you have that need in the future? If you do, you need a door.

No door here. Our laundry room is on the other side of the house. Didn't want to have to open doors as I was carrying groceries in. And maybe it will motivate me to keep the mudroom semi-neat.

We put in a pocket door. It's rarely closed, but at least we have that option.

No door here, just a framed doorway. Based on what the trim around the door to the garage looks like, I think if we had done a door it would look pretty based up. If you want to be able to close it off I would consider a pocket door.

If you live in a climate of extreme weather, I'd put in the door to give you an extra "airlock" to keep the heat or AC in. Otherwise, I guess it depends on whether the view into the mudroom from the rest of the house is something you think you'd rather be able to hide from time to time, and whether you think an extra easily-moppable room with a closable door would be valuable to you.

Are you an animal lover, for example? Leaving the door open gives you one less obstacle to maneuver when bringing in groceries, to be sure, but it also robs you of a good place to seclude sick pets, mud-covered dogs, etc. Only you know if you're likely to have a need for such a space, or to consider it more valuable than the loss of the ability to travel unimpeded from the garage to the kitchen.

We have a pocket door going in our planned mudroom. It will likely be rarely closed but we too wanted that option. Also, it is near our back door and we will likely put the dog in there sometimes after her bath, etc.

We have a mud room/panty between garage and kitchen...no door and I think I'm going to be happy with that arrangement. Easy to gather panty supplies and free flow for grocery carrying, etc. Also a solar tube it located here so some of that light spills into kitchen.

We did as apophrenia suggested: "give you an extra "airlock" to keep the heat or AC in," and it usually is closed. Also, when I am bringing groceries into the mudroom from the garage, it gives me a landing space before my cat comes to me so she can't get out.

we have a door and it has helped in several ways. It is typically kept in the open position during the daytime, closed at night:
1. Hiding the mess. No matter how neat and tidy you are, eventually the mudroom becomes messy. and when you get unexpected guests, sometimes it's just easier to close the door!
2. corralling the kids!!!! it's been a blessing to get all the little ones into the mudroom and then being able to CLOSE the door so that none of them sneak away while we are trying to leave :)
3. ditto to the extra layer of airlock from garage.

Thought we'd like the open doorway look between kitchen & mudroom in our last house, but ended up wishing we'd put a pocket door in. Like many other posts-it's nice to have the door just in case unexpected guests come over or your pet is sick, etc.

I also requested a pocket door from Mudroom to HearthRoom/Kitchen area. I personally feel that Muddy boots, strewn jackets and toys, and random odds and ends do not need to be on display for everyone to see.