I'm a long-time elite member of United Airlines because I'm from Washington, D.C., where Dulles is a major United hub. I would recommend you join the airline that most serves where you are traveling.
Several years ago I made the major mistake of signing up for every airline's program, so I now have membership in at least a dozen frequent flier miles. As a result, I have miles spread out across several airlines and that's not helping at all. My No. 1 tip would be to sign up for membership in one airline in each of the three major alliances: Star Alliance, OneWorld and SkyTeam. I mostly use United (Star Alliance), American Airlines (OneWorld) and Delta (SkyTeam).
The important thing to do is sign up BEFORE you book your flights. I'm amazed at how many frequent fliers I've met who have never joined the plans. It's like throwing away free money! It's 100% free to join. And also there are often surprise perks. On overbooked flights, I've received priority and occasional bumped up to business and first class a few times just for the simple fact that I was a frequent flier member and the other passenger was not.
Personally, I find upgrades to be more valuable than free flights. For example, let's assume that a summer roundtrip flight between London and New York is $1,000 in economy, and $3,000 in business class. If you use your miles to book a free flight to New York, you'll use about 60,000 miles and save $1000. But a typical upgrade usually only requires 15,000 miles. So if you buy a $1,000 seat out-of-pocket and upgrade to business with your miles, it's like saving $2,000! Plus you're using less miles to fly in luxury! Make sense? It's a lot easier nowadays to use miles for upgrades than for free flights. And unless you plan WELL in advance, it's nearly impossible to get free transatlantic flights during peak seasons.
Another tip: Sign up for your favorite airline's credit card. You will usually get 1 mile for ever $1 spent in charges. I buy practically everything on my credit card from groceries to clothing and hotel rooms, and pay off the balance every month. Often you will get bonus miles for using that credit card to book your airline flights.
One last note: I agree with previous poster about complaints on British Airways & American Airlines. They are very stingy when it comes to UK-US flights. Personally I don't care for either airline. United and USAirways are better options for Londoners, both of which are StarAlliance. I prefer USAirways as they fly out of Gatwick, a MUCH nicer and more relaxed airport than Heathrow. (FYI Karin, United flies nonstop from London to San Fran).