Is there a limit on the number of games (games in progress) that one can play?  I've noticed that some players have hundreds of games and I am not sure whether this is the real reason for invoking "vacation" option (can't make a timely reply on every game in progress.

No, there is no site limit on the number of games one can play. But most people have a limit to the number of games that they can actually play well. As for vacation, what you may be seeing is if the members are premium members, then vacation time gets kicked in automatically once they start to run low on time for any of their games.

thank you

You are right. I have seen players with more than 27 games going at the same time and all the time "my move" is lit in more than half of them. I try not to play with them, 'cause the game could last a lifetime.

I have more that 27 games going and I move quickly, I think once you get over 50-60 is when it starts slowing down a little.