I would leave AT LEAST 2 hours for a connection in the US (where your first flight originates from outside the US). As others have said, you will need this time for clearing immigration, reclaiming luggage, clearing customs (although that rarely takes much time), rechecking your luggage (hopefully your airline has a transfer desk just the other side of customs) and getting to your departure gate (sometimes in another terminal...). I wouldn't like a connection of under 2 hours, 3 hours can be better (allows for any upsets and allows for a rest and a drink/bit to eat in between flights...).
A "through ticket" (i.e. your connecting your flights on the same itinerary) WILL protect you to a certain extent - if you miss your onward flight, they WILL put you on the next available flight. BUT you have to be aware that may not be until the next day (i.e. your connecting flight was the last of the day or any later flights that day were sold out...). Also, if your connection is tight, there is a high chance that your checked luggage may not make the connection even if you do... so could take a day or two to catch up with you. The longer your connection, the more likely your luggage will get to your destination when you do
Obviously those are pesimistic views, but things to be aware of...
You don't need as long a connection when exiting the US (since you don't have to clear customs/immigration between flights... and you probably aren't as worried about your checked luggage either). But I would still leave about and hour and a half or so (depending on where you are connecting and any changes of terminal required...).
We have used international/domestic connections quite a lot (most often on seperate tickets - so we haven't been protected) with few problems... but it is good idea to know the risks involved.
Boo