For a smooth online gaming experience, it's generally recommended that you have a broadband speed of at least 3 Mbps (Megabits per second) for most games. However, if you’re playing high-demand games, especially in multiplayer mode, you might need speeds of 15-25 Mbps. Remember, this is per player. If you have multiple people gaming in your household, you'll need to multiply this by the number of players.
Furthermore, it's not just about download speed. Upload speed and latency (ping) are also important. Upload speed of at least 1 Mbps is recommended and a ping rate under 150 ms, but ideally less than 100 ms for a more responsive gaming experience.
These are just general guidelines and the specific requirements can vary greatly depending on the game, the gaming platform and the number of players. Always check the specific requirements of your chosen game.