It's your guitar/banjo/mandolin/nyckelharpa. . . and if you want to leave stuff fastened to your headstock, it's up to you, but I'll admit to not liking the look of tuners, capos, cigarettes and unclipped strings (sometimes all on the same instrument), especially one with an attractive shape or some tasteful pearl inlay. These same folks will sometimes even have those stick-on pick holders as well.
If you're one of the folks who like to do this, I'll still jam with you, and won't even spend a lot of time thinking about how ugly these things look.
I'll also admit to having most of my cases covered with stickers, even though some of the musicians I play with think it's ugly.