Well, here is a different one.
Most of the answers so far are derived from playing a heavy action packed game, and probably that was the real direction the question wanted the thread to take. But, if we are talking intensity as sensations or emotions existing in a high degree; forceful or extreme (invoking the dictionary's terminology), then to me, nothing has ever beaten the last sequence of The Longest Journey: Dreamfall.
Purely adrenaline-wise? The very first time I fought the final villain in Return to Castle Wolfenstein. It was one of my first games and my inexperience added to the thrilling mix. The battle raged for almost an hour.