The London City Pass is worth it BUT ONLY if you plan your route very carefully. DO NOT get the transportation part added to the card, only purchase the CITY PASS that allows entry into places.
First you have to figure out what you want to see because, as many people have stated, several places are free. So if you get a City Pass, in order to maximize it and truly benefit from it, you have to focus all your time and energy on using nothing but the pass and using your other days in London on the free places to see.
You have to pull out a map and plan on hitting everything in order. You won't use the card wisely if you spend most of your time zig-zagging across London to get from place to place. If you decide to use the pass to see Windsor Palace, Wembledon and Hampton Palace-that is literally a day of travel and site-seeing as these places are way south of London proper.
I lived in England and visited London for a number of years before purchasing this pass. It was definitely worth it for my family but then again we'd already spent numerous trips enjoying all the things London has to offer that were not included in the pass.