For the last few years I've been making a lot of international flights. Most of the long flights have been between London and San Francisco or London and New York. I've also made a trip between London and Hyderabad, India.
I've found that there are some universal truths to getting a good airline experience. The most important of those is that you should fly direct. If you can't fly direct then you should do the short leg first.
I fly direct to save time and hassle. Since I'm flying from London, that means that I can usually fly anywhere in the world on a direct flight (except for Hyderabad). Flying direct means that I can check my bag once, and know that once I'm on the plane all of the hard stuff is over.
When you do have to connect there are usually two options with regard to when you take the short leg of your itinerary.
Upgrade, has an article on strategies for making international connections, and I totally agree with what the author says. Basically it comes down to always making your short trip first. So if you are flying from the USA to Europe and you have to make a connection, do it through an airport in the USA. That way you can sleep on the second flight and when you wake up you are done.
Also, as the article points out, when you are flying into the USA you have to go through customs and immigration at the point of entry to the USA, not your final destination. So, if you can swing it, you should set up your return flight so that you do a short flight in Europe and then a direct flight back to the USA.
There are some exceptions. For example when I fly to India, I prefer to always do my short flight in Europe. So I fly from London to Frankfurt, and then fly direct from Frankfurt to Hyderabad. The reason for this is that I find navigating and killing time in the Mumbai airport to be a little painful (there aren't many restaurants, and there isn't much to do).