The classic Uno game & a more adventurous version are available to be played among groups, in teams and you can even host a tournament!
This category game allows you to host a challenge between a closed group of people (by sharing a code).
Words/Crosswords/Chess/Boggle With Friend:
This website has 4 different games which can be played online between people. Most are one-to-one games but you can use them by creating teams.
Kahoot! makes it easy to create, share and play learning games or trivia quizzes in minutes. You can host a live Kahoot! by sharing a screen while participants answer on their devices.