It depends on exactly what type of social interaction you're looking for. There is a very broad category of games known as "party games" which loosely meets your definition. Party games tend to favor social interaction over luck and strategy (in many cases, no equipment at all), tend to require less per-player equipment, and tend to be flexible in the number of players they support. Take a look at the linked Wikipedia article for more information, or you can browse the party games category or subdomain on BoardGameGeek. A somewhat older category, that has considerable overlap with party games, are parlour games, so you can look there too.
Within the broad category of party games, there are a few subcategories. The one you mention, Werewolf (also known as Mafia), is known as an "uninformed majority" game, in which some people have information that the rest of the players are trying to figure out, mostly through social means. There's another thread on games with uninformed majority mechanics, though many of them are more traditional board or card games. Other party games in this category include Are You the Traitor? and the How to Host a Murder series of games.
Other subcategories of party games include word games, creativity games, and icebreakers, with some overlap between them. Word games tend to involve someone having one or more secret words, and giving clues that other people use to guess the word or definition. Creativity games involve being given some sort of creative prompt (a pair of words, a picture, an object), and doing something creative with them, such as telling a story, drawing a picture, inventing a product, or the like. Icebreakers are games in which people reveal facts about themselves, in order to provide a structure to break the ice and allow people to get to know each other better.
In the word games category are games like Contact, in which one player has a word, gives the first letter, and players try and discover the word by giving clues that indicate their guesses, making the player who has the word try to figure out what word they're guessing or give up another letter if they can't. There's also Taboo, in which someone is given a word, and has to get their teammates to guess the word, but has a list of other words that they cannot say while describing it.
As both word games and creativity games, there are games like Balderdash or Fictionary in which you pick an obscure word, one person gets the real definition, and a few people make up definitions. The other players have to then figure out which definition is real. There's Charades and Pictionary, in which you get a word or phrase and must describe that to your teammate, in charades by acting it out, in Pictionary by drawing it. Apples to Apples is a very popular party game, which might be considered a word game, in which someone draws a card with an adjective, and everyone must play nouns that closely match that adjective, at least according to the person who is the current judge; due to the limited selection people have to choose from, you get some very amusing juxtapositions in the process.
Some other creativity games include The Big Idea from Cheapass Games, in which you get pairs of words such as "electric pants" and must describe that as an invention and get people to invest in it, Why Did The Chicken? by Kory Heath in which you must make up jokes, and Nanofictionary by Looney Labs in which you get cards for Characters, Problems, Settings, and Resolutions, and must combine those into the best tiny story.
Then there are the icebreakers. These are games like Two Truths and a Lie, in which each person in turn will tell two truths and one lie, and the other players have to guess which is the truth and which is the lie. There's Never Have I Ever, in which each person says something that they've never done, and everyone who has done it gets a point (or has to drink, as it's commonly played as a drinking game, however it's not necessary to play this way, you can simply keep score instead); if only one person has done the thing in question, they need to tell the story. There are many more such games.
A little further afield than what you're looking for, I think, but still involving more social interaction than traditional game mechanics, are negotiation and alliance type games like Diplomacy. I have a question open now looking for "lighter" versions of it, and there are few games that look promising.
Another somewhat further category of games, that can be more social interaction based, is roleplaying games; some creative one-shot roleplaying games can have a lot of the same elements of games like Werewolf, with intrigue, cooperation, and backstabbing. I recall one that a friend ran in which all but one of the players were minions of the dark trying to take over the world, but there were two dark lords, a Satanic type and a Cthulhoid monster, competing with each other, plus all of the minions were competing to be favored by their lord. So everyone had three sets of enemies; the Good, the other Evil team, and the other minions on their own Evil team. It was quite the treacherous game, involving lots of intrigue and social interaction; it turned out that Evil had too much infighting, and Good won. There's an entire other StackExchange for roleplaying games, so check in there if you want to learn more about them.
So yes, there are a lot of games that have more social interacting and less traditional board, card, and dice mechanics. I hope I've given a good overview; feel free to ask about a more specific category or game if you want more information.