I know that this question has been discussed a bit in numerous topics about SC2, but still perhaps there is a possibility how to see the elapsed game time ingame? Or is it perhaps planned in future SC2 patches?
For campaign missions, you can save and reload the mission then read it on the loading screen. I'm mainly interested in this for multiplayer games, however.
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Edit: There is now an in game clock feature. It can be enabled by going to options, gameplay, and then enabling the in-game clock. The below is old information and no longer relevant.
There is currently no way to view the time elapsed in game. The lack of this has led to numerous threads requesting the feature on blizzard's forums. There appear to be no plans currently to add it, but I would not rule out the possibility of it being added eventually given all the requests blizzard is receiving.