Botticelli is a good one among people with roughly equally good general knowledge. The version we play on this board is a bit stricter with its rules, I think the best way to play it face to face with people who are averagely knowledgable is this. Someone chooses a well-known person or animal (past or present, living or dead, fictional or not), the principle being they are supposed to be ‘at least as well-known as Botticelli’ (YMMV on what that actually means). They reveal the initial letter of their name (up to you if you want to make this last name, first name, or could be either - the latter is best IMO as it gives the widest scope). Then everyone else interrogates them, but unlike in 20 questions, direct questions are not allowed to begin with. Instead, players may ask indirect questions such as “Are you a pop singer?” or “Are you a current NFL quarterback?” (it’s up to the group how specific, or otherwise, the questions should be). The questionee has to reply with a valid answer matching their chosen letter, for example if the letter was “B” they could respond “No, I am not Beyonce” and “No, I am not Tom Brady” respectively. If their chosen person is in fact in the category asked about (e.g. the person to be guessed is William Shakespeare and someone asks “Are you a dead playwright?”), they can reply such as “Yes, but I am not George Bernard Shaw”. If they are unable to name a person with the correct initial in reply to the question, and the questioner can do so, the questioner is then entitled to ask a direct question such as “are you alive?” or “are you male?”. In this way, eventually the right person will be guessed. So a nice variant on 20 questions.
One I have never played but seems like fun is known as Kolodny’s Game. Similar to one of the previous suggestions, the target players makes up a ‘rule’ like ‘Answer “yes” to any questions containing the word “you”, otherwise answer “no”’. Everyone else then asks questions to try and work out what the secret rule is. This can have amusing consequences, for example: “Have you ever been unfaithful to your wife?” “Yes”.
Similar to the alphabet games already mentioned, but with a bit more tactical interaction: pick a category (e.g. “animals”, “countries”). First player names something in the category, second player has to name something else in the category that begins with the last letter of the previous answer. With countries it is easy to get into long loops of A…A countries (being careful to avoid continents). For animals, an answer of “wolf” is likely to be met with “fox”, giving the next player a problem.
Finally I’ll offer a simple word game (probably best with 2 players but can be any number): first player names a letter, second names another letter, and so on. The object of the game is to not complete a valid English word. But, a valid word has to still be possible from the letters already played. Example game:
Player 1 “G”
Player 2 “H”
Player 1 “O”
Player 2 “S”
Player 1 “T”
And player 1 loses for spelling “ghost”. Alternatively, if Player 1 had said (for example) “W” on their final turn, Player 2 wins unless Player 1 can name a valid English word beginning “ghosw”.
Credit for all the above goes to a book of mine called “Word Games” by Peter Newby.