Zipper is a yellow rabbit with a white muzzle, visible bucked teeth, overalls, and a sun visor. There is a zipper on the back of Zipper's overalls which may be the source of Zipper's name. It is easily visible when seen from behind, which causes Zipper to turn around and comment saying not to look at the zipper, as it "spoils the magic". It's a running joke that villagers think he is someone in a costume though he has defended his appearance saying it is, in fact, not a costume. In Pocket Camp, he seems sensitive about it, claiming it's rude to call it (his appearance) a costume and that this is just how he looks.
In City Folk and New Leaf
Upon being approached, his theme will begin to play and Zipper will begin to dance. As the player leaves the Town Plaza the music and dancing fades and Zipper will sigh heavily. Zipper will ask the player to search for bunny eggs that are buried around town. Opening these will reveal a "surprise", Zipper says, but after constantly talking to Zipper without finding one, Zipper eventually will tell the player to look for bunny foils, which are also called prize tickets. Zipper will give the player Furniture from the Egg Series or Zipper's picture each time the player finds one bunny foil or grand prize ticket (respectively) inside an egg and gives it to Zipper.
During the event, villagers will usually speak of Zipper in a derogatory manner. Normal villagers appear to be scared of Zipper or worried about his health. It would appear Zipper is unhappy with the choice of uniform and job, by mentioning that Zipper wants a new job under their breath and will occasionally mention how uncomfortable it is under the suit - also, under their breath.
After the Welcome Amiibo update for New Leaf, when visiting Zipper's RV, the description will say, "Camping gives Zipper a chance to finally get out of that stuffy old costume and- er, we're being told in no uncertain terms that it is NOT a costume."
In New Horizons
In New Horizons, Zipper arrives on the island on the first day of the Bunny Day event to tell the player about the festivities and present the Bunny Day bed DIY recipe, but asks that the player keep his visit a secret. He will remain on the island for the entire day. Zipper returns on the final day of the event and can be found in the Resident Services plaza, where he will offer additional crafting recipes and exchange eggs. Zipper remains guarded about the zipper on his back, and villagers will mention teasing him.
Zipper shares a birthday (3/11) with a rabbit villager - Hopkins.
Throughout the series, Zipper has staunchly expressed that he is, in fact, /not/ wearing a costume, though there is an obvious zipper on his back. He even alludes to this in New Leaf: When players talk to him from an angle that makes him turn to reveal the zipper, he says not to stare at it, as it'll "ruin the magic".
Warning: Theory starts here.
Fans have come up with many theories as to Zipper's true identity, though many of them are easily debunked:
Phyllis: People theorize that Zipper is Phyllis in a costume due to their similar habit of making asides in grayed-out text, about how much they dislike their jobs. This has been debunked in all games prior to New Horizons, as Phyllis is still present at her job in Town Hall or the Post Office, or in The Roost, whenever Zipper is present in the player's town.
Tortimer: People also theorize that Tortimer is Zipper, but he too is present at the Town Hall or in Island Tours (in New Leaf) when Zipper is present on Bunny Day.
Both of these theories have not yet been debunked in New Horizons, as neither Phyllis nor Tortimer have made appearances as of the 2020 Bunny Day event. It is theoretically possible that, in this game, either of them actually /are/ Zipper. Then again, this wouldn't make much sense, given that Phyllis and Tortimer were in past games.