Via Pharyngula, I came across this fascinating graphic from a study commissioned by the Wall Street Journal that shows how time is distributed in a typical 192-minute American football game. It turns out it is only 11 minutes or less than 5% involves actual play action. I think the instant replays (sometimes five or six at different speeds and from different angles) give the false impression of there being more action than there really is.
Baseball is not much better, having just 18 minutes of play out of a total of 178 minutes or about 10%
Having grown up on rugby, when I came to the US I was amazed at how slow football was. It was highly amusing to see some football players being given oxygen after just one run when rugby players seemed to be in motion the whole time. I initially thought that rugby action must be at least around 80-90% but it turns out to be much lower but at around 44% is still much higher than football. I suspect that soccer has a greater percentage of playing time since the rules are simpler and there are fewer set pieces but I could not find any data.
I suspect that even notoriously slow games like cricket would have a greater percentage of action than American football. In cricket, one would have to count just the time from when the bowler begins his run up to deliver until when the ball is dead. But I could not find any data for this either.