Gateway games generally have simple rules that are easy to teach non-gamers in order to attract new players into board gaming as a hobby. But they are great even for seasoned gamers to start off your game night or play between heavier games.
Tsuro: The Game of the Path
Jaipur (New Edition)
Ticket To Ride
Clank! In! Space!
Imhotep: The Duel
Survive: Escape From Atlantis 30th Anniversary Edition
Lords of Waterdeep
Tokaido: 5th Anniversary Edition
Deep Sea Adventure
Forbidden Desert: Thirst for Survival
The Resistance: Avalon