The airlines have what they call a minimum legal connection time that they use to determine if they will sell you a ticket with specific flight combinations based on odds of a successful connection in average conditions. That list of times is not widely circulated because it typically contains a bunch of different variables ("except for 787 aircraft arriving at Kuala Lumpur, Denpasar, or Changi Airports on Tuesdays and Wednesdays in months with R in them") but you can often find relevant parts of it in assorted places on the 'web like Flyer Talk's hub airports threads.
Frequent flyers also refer to the 'minimum sensible connection time', which typically is a lot more of a time buffer between flights.
My risk tolerance for short connections is highly variable and based on 'so what happens if I miss a flight?' I will gladly go a 40 minute domestic to domestic connection in ATL if A) the price is right B) my first flight is getting in by 1:00pm or so leading to C) I've got 3-5 other flights that day I could be rebooked onto if I miss my original connection.
I have a lot lower risk tolerance if I'm trying to connect to the last and/or only flight of the day to a destination. I've currently got a ticket for Zurich next summer where I wouldn't take less than a 3 hour layover connection in Atlanta because there is only one daily non-stop from Atlanta to Zurich and I have extended knowledge of the ATL's tendency to have summer thunderstorm delays.
I've done right at the MLCT coming home from Europe (took it to make a frequent flyer ticket work for a reasonable number of miles) Despite a number of small ICE and TSA delays, we made it to the next gate with time to spare, but it was still stressful and I'd really want 2:30 or so to clear immigration at a large hub.