It is best to not book connections that are too tight and it might be an issue, but things can go wrong. When they do, if possible I will ask the FA on the first planeto let them know I am coming (I don't think this usually does anything, but can't hurt), I do run to the next gate, and I try to know where that gate is and how to get there from the gate I am landing at (gateguru has good maps, as might the inflight magazine). This is especially true for an international connection, and when I am trying to keep a business class upgrade. There will still be times when you don't make it, and if the connection was on the same PNR, they will rebook, but it is not always a smooth process, so worth making an effort to avoid it. That said, there are worse places to kill 6 hours than most large international airports. But if there are no more flights that day (also, it is a good idea to be aware of potential backup flights - staff are not always good at finding them, especially if not on their metal), having to stay overnight is generally unpleasant.

I think the first time someone misses a flight because they opted to do some shopping or grab a nice meal in the airport is probably the last.