Admission is included in the London Pass.
This is a fascinating and historical landmark that is over 900 years old. The Tower of London was built as a palace, then became a prison and fortress. You can see how early kings lived. You get to see the carvings prisoners made in the walls. You get to see an exhibit of ancient armor and weapons. You can see where Henry VIII beheaded two of his wives (Anne Boleyn and Catherine Howard). And, most importantly, you get to see the Crown Jewels. The actual crowns (there are 2) that were used by Queen Elizabeth II at her coronation are here, as well as several other crowns, some mind-boggling silverware and other precious things. You also get to see the world's largest diamond. There is an interesting exhibit about the evolution of the crown, how it is made, and how the largest diamond came to be part of the Crown Jewels.
I would highly suggest going on a guided tour with one of the Yoeman Warders of the tower. These tours start right at the entrance. Beware, the last tour starts at 3 PM. There is also a series of several short (about 25-30 mins) illustrated (with slides) talks by a Yoeman Warder, that is held daily at the Lanthorn Tower (one of the many actual towers inside the compound, which you can easily find once you go inside and are issued a map of the place).
Don't do anything bad at the Tower, because Yoeman Warders are actually a type of military officers and do have police powers on the territory of the Tower, despite the nice costumes they wear.
This is also the site of the actual Traitors Gate (see entry on the London Dungeon) where prisoners were brought into the Tower by boat.
If you would like to see the Ceremony of the Keys, which is one of the oldest continuing ceremonies and takes place in the evening, then be sure to write ahead of time (at least a month) to: The Ceremony of the Keys, Waterloo Block, HM Tower of London, EC3N 4AB. You must enclose a stamped addressed envelope and request the date that you would like to attend.
Because of its age, the Tower is full of cramped, circular staircases. Keep this in mind when you come to visit.