Dutch Blitz, also known as "Ligretto" and a bunch of other names.
It plays 2-12 players very fast, since all play is simultaneous. I've heard it called "speed solitaire", and that's a pretty apt description.
All the player are trying to clear away their piles into a common area, so you have a lot of high-speed interaction, but of very brief length. Mostly in the nature of "hey, I was gonna do that!".
Rounds take between 2-10 minutes, and there's a downtime of about 1-2 minutes while the scores are tallied. Apart from that, all the players are playing all of the time.
The downside to the game is its speed. There's a lot to keep track of, and many beginners will get confused. It the job of the experienced player to get them to stay calm and focus on the basics, until they get familiar enough to "see everything". That only takes 1-2 rounds.