Personally, I hate' em! Nothing like keeping a clean house and having people track (back and forth) over a thoroughly soiled and dirty entryway carpet/mat, then track that same dirt and soiling (in it's entirety) through ones clean house!
Inspiration for me starting this thread? Company and guests (continually) passing their off-the-cuff comments (my way) related to, "why don't you have a carpet/mat down in the entry, Margaret"? "You should have a carpeted floor-mat down in the entryway, Margaret". No, I shouldn't! And, no, I don't want one!
I gave up on keeping an entryway rug/carpet in our home (many years ago), due to the opening reasons I stated. I prefer a floor that can be washed/scrubbed, instead. Sure, a narrow carpeted runner tucked neatly against the wall (out of the way of where everyone walks and tracks-over), is nice for storing footwear, but IMO having an entryway carpet that seldom (if at all) ever gets cleaned, doesn't make sense to me.
What's your take on the matter? What have you come up with in your home as to entryway flooring/material?