We used the 3 day London Pass last year and felt like we got our money's worth but didn't try to maximize the value beyond just going to the places we really wanted to see (our 7 year old was with us, so his interest was a big factor, too). I did a lot of pre-planning for our itinerary so we weren't crossing the city unnecessarily in a day. Here's what we did with and without the pass:
Day 1- No pass use. Walk around the city and get bearings, see non-paying sights like Trafalgar Square, St James Park, outside of Buckingham. We did the Ghost Bus tour in the evening, it was pricey but a lot of fun.
Day 2- Activate pass. King's Cross Platform 9 3/4, London Zoo (Pass), British Museum.
Day 3- Tower of London (Pass), Thames boat ride (Pass), Westminster Abbey (Pass), theater in the evening.
Day 4- Hop On Hop Off bus tour (Pass), London Walks walking tour (discount with Pass), Natural History Museum, we were going to do Kensington Palace with the pass, but instead just walked through Kensington Park and took the kid to the Princess Diana playground, which was amazing and was one of the highlights of the trip for my son.
If we'd had one more day I would have used the pass for Hampton Court / Kew. I liked that the pass let us fast-track the line in a few places, and I liked the budgeting ease of having pre-paid for entry to all those attractions, that was a value beyond just money saving for us. Also, we got to the Tower of London at opening time, there was no line and hardly anyone there! It was fantastic. Followed Rick Steves' advice to see the Crown Jewels first, and we practically had the place to ourselves. By the time we left the Tower the crowds had arrived. I would say don't forgo the free museums just to pack in sights on the pass that you might otherwise not be super psyched to see, as long as you're using the pass once per day and pick two of the four days to do more than one pass attraction, you should get good value for the pass.