I think an arched door could look charming, depending on the style of the rest of the house. Can you get arched pocket doors? Wonder how that works... interesting! Not sure I have ever seen one. Sounds cool.

Beware that arched glass doors can be very expensive!

We have an entrance door that is arched. The surrounded openings are rectangular. Looks fine. We also have some arched openings in our family room mixed in with regular openings. I like the character.

It will look strange any time it is not completely open or not completely closed.

It depends on the style of the architecture. A special door many times indicates a special room. If your pantry is the most special room in your home there may be a need for some adjustments.

Many times a compilation of 'liked' details in architecture can create train wreck void of continuity.

Choosing something deliberately different than the styke contininuous elements that make up tge home is for a focal point that is a big feature that you want to draw attention to. Not everyone wants to spot light the location of their pop tarts and dusty cans of beets.

On behalf of beets everywhere, I protest! I agree, it has to go with the architecture-- I have a small cape (circa 1948) that has one arched doorway thati s the only arch in the house. It's very typical of that era and location. I like it but I'm sure some would not. There are other homes in the area that have the original wood arched entry door, but that refrain is not continued through the house. Nonetheless, I find them charming as well. In the photo posted, I like the door. The rest of the details in the photo are obviously nice and functional, and yet, I find them boring :) However, all those other details are exceedingly popular. Of course, I like beets (but a hard no on the pop tarts) so that tells you something about my taste, or lack thereof.

My father was a young child in Europe during the war. He learned to like things that would have been used as animal feed in normal times. They were lucky they lived in the countryside and could grow some food. In his 80s now and still likes turnips, parsnips and beets!

If using that pantry door, I would prefer that the arch be repeated somewhere else in the house and not be the only arched item in the house.

I had pocket door(s) in an arched opening. Paired doors in an arched opening will work because you can take out the stop, and pull the rectangular door out of the pocket and get it out without tearing up the wall. For this pocket door to be success, the door would have to be completely finished and then built into the pocket and the wall finishes put over it. And woe betide it if something happens you would need access to the pocket, at least in part to get this whole thing out. A pocket would not work well in the position that door is in.

If you want to do an arched door like that, just do a conventional hinged arched opening. It will be much easier.

And I don't want to assume anything about your budget, but the millwork around arched doors or windows, particularly if you want it to match the profile of the other casings in the house . . . semi to full custom.

I’m agreeing with most - a single arched door could be an interesting design element. At seeing this picture, I’m wishing my pantry door with reeded glass panel also had an arch. I have arches to 2 hallways & a really wide one between kitchen / eating area & great room but no other arches. I had to think about @bpath comment that ”It will look strange anytime it is not completely open or not completely closed.” Why would we leave the pantry door standing open?

@KW do you have a pantry door? 
My pantry door is open almost 100% of the time unless we have company and I make an effort to close it.  The pantry is a room you have to access repeatedly when you cook, and opening and closing that door every time you enter and exit... well, maybe you can make that happen but I cannot. I really wanted a double acting swing door in my pantry for this reason but my pantry isn't big enough. 
OP if your pantry is big, look into double acting swing.  Can't comment on the arch.

@anj_p yes - i do have a pantry door with a reeded glass panel so the contents are obscured but if light on inside pantry it is visible. My pantry door is kept closed unless I’m standing inside of it. As a point of reference, all my closet doors are kept closed too. I’m usually a tidy person but not compulsive about it. The arched door in picture would need to stay closed to have access to counter on right of door & though I imagine that’s not the cooking prep counter, I’d be keeping it closed too! 😊

This is what it will look like. Because remember a pocket door fits in a track at the top, so it will be a rectangle.

According to my family, both two and four legged members, the pantry is the most important room in the house. I think it looks charming.

Thanks everyone! Appreciate all the feedback. I'm thinking I'll probably go with a more standard framed door, although I love the look of the arch, I'm not sure it's the place I'm trying to make a statement. Thanks for all your thoughts and tips!!!

My apologies to all! My finger slipped and it looks like I reported this as spam. Don’t know how to reverse that!