I do not want to read all the responses, but the 'known' board games suggested are quite boring. There is a massive world of board games that are extremely exciting.
If you suggest what hobbies or interests you all have, the ages of your children, I could suggest a whole load of games that could interest them.
The rules are a little more complicated than monopoly (an awful game), but most have 'how to play videos'. I can point you to them.
For example, a great family game is: Long Shot Dice Game.
If you all like Downton Abbey, a fantastic game we just played today is: Obsession.
If your children are older (15+) and like reading and mystery solving, then another game is Sherlock Holmes Consulting Detective. (We have played 4 of the 8 in the box, only solved 2 cases, but have come close in the other 2 and totally enjoyed the experience.)
Another detective game with very simple rules, a kind of hide and seek game is Scotland Yard. Older children might prefer Letters from Whitechapel.
A deck-builder game that is very cheap, but brilliant, is Star Realms. If there are 4 of you, get the 'Frontiers' box.
Another great set of games is the Clank!! universe. You are trying to delve into a dungeon or space station, trying to be as silent as possible, while getting loot. If you like fantasy go for Clank Catacombs. If you like sci-fi, go for Clank in Space
I am interested in head to head wargames. One of my favourites is Julius Caesar. Only 8 pages of rules, loads of videos of how to play. Absolutely fantastic game. Probably best for 15+ years of age.
Another great wargame series is Axis and Allies.
If you go to Waterstones, there are a lot of interesting games, usually in their basement. Let them look at the boxes, see what takes their interest, get a list, I would be very happy to help. I will tell you how difficult the rules are. Link you to some videos of them being played.
If you tell me which town or city you are close to, I will give you a list of the specialist game stores in your area. They are called FLGS (friendly local game stores) and they are always happy to help, making suggestions of starter games. They would even teach you the rules.