My trivia game of choice is Superbuzzer, available as an app on iOS (and, I assume, Android), or you can play it on your computer through Facebook. It's got bits and pieces of many games mixed together - I can see pieces of Jeopardy, The Big Showdown, Split Second, and even Runaround.
Round 1: Six contestants, five questions. Three points for the first correct answer, two points for the second, one point for each correct answer thereafter. No penalty for incorrect answers. Highest four scores move on to Round 2.
Round 2: Four contestants, five questions. One point for answering each of the first two questions correctly, two points for the third and fourth questions, three points for the fifth question, plus one extra point for the first correct answer. However, you're penalized the same number of points for incorrect answers. Highest two scores move on to Round 3.
Round 3: Two contestants, six questions. Seven seconds to answer the question; the contestant who gets the correct answer stays with the same amount of "energy" they started with; the other contestant loses energy (depending on how quickly the other contestant answered correct). No penalty for incorrect answers, no limit to the number of times you can answer, and if both contestants buzz in at the same time and get it right, they both lose energy. The first contestant to lose all their energy is knocked out; if neither contestant loses all their energy, the one with the most energy after six questions wins. (It is theoretically possible to have a double knockout, but I've never seen it.)
Winner gets a free game at the next level (there are five levels overall); also everyone gets a free game every 12 hours (but you can't hold more than one game in this manner at a time).
It's fun playing against others, especially overseas contestants. The bad news is the questions are fairly UK-centric; lots of soccer and Harry Potter.