My first thought was for connecting airports in Europe. Although I've arrived or departed from four airports in Germany (FRA, MUC, STR, DUS), I've only connected in two (FRA and DUS). Düsseldorf was by far the easiest connection. Both my arrival and departure gates were on the same level in the same building, at opposite ends of a long hallway with emigarion (outgoing passport check) just a gate in the hallway. Easy-peasy.
In January 2002, I changed flights in Frankfurt (from MUC, to DEN). Everything was in Terminal 1, but we arrived at Concourse A and left from Concourse B. Thanks to the connecting tunnel and good signage, everything went smoothly, even with enhanced security (it was just 4 months after 9-11).
I've flown in or out of Munich multiple times, but never connected there. I like it's layout and wouldn't mind connecting through Munich.
As for the US end of a trans-Atlantic flight, I've flown directly to/from Denver multiple times but also had connections in Newark, Philadelphia, Atlanta, Washington, DC, Chicago, and Detroit. Every connection had it's own hassles; I will fly direct from/to Denver any time I can.
My biggest problem with an arrival connection in US airports is that, because they want you to have access to your checked luggage at customs,, and therefore to things you are not allowed to carry on to the next flight, you are required to go back through security if connecting.
Philadelphia: the same as someone's comment about JFK, half the people in security seem to have no other assignment than to scream at passengers. And, the airport is huge, and linear. I arrived at Termainal E or F, and flew out from A. I don't think there was a shuttle at the time; at least I didn't see any signs to one. The good new was I had four hours to transverse the airport and make the connection. The bad news was I had four hours to make the connection.
Newark: So the next time I had an eastern connection to and from Europe, I used Newark (no more Philly for me). At the time we had to change terminals from arrival to international departure, and the shuttle is outside security. We had to go back through security to get into the international terminal.
Atlanta: I once flew to Europe through Atlanta (Delta had the only non-stop flight to Stuttgart). The problem wasn't Atlanta's layout. Connecting through Hartsfield was a breeze, but we had to fly for almost 2 hours to get over the New York/Philly area, which would have been about the same time to as Atlanta, on the way to Europe. So it added a lot of time to our travel.
I think as far as flying to Europe, not including a direct flight from Denver, I would prefer ORD as a connecting airport.
As for domestic flight connections, Phoenix has got to be the worst.