Ok, so this is my first hands on review and its also a warning. I've only recently visited Paris, and of course, the Eiffel Tower is a must see for every tourist and, as John Graham-Cumming says in the Geek Atlas, also for every geek. He is right as the whole Tower can be seen as a monument for science, with the names of famous french scientists (Foucault, Arago, Fresnel,...) written around the Tower and a bust of Gustave Eiffel at its foot.
Now the warning: If you decide to go up, you spend 99,99% of your time with waiting. Waiting to buy a ticket to go to the first balcony, waiting to get into the elevator to get onto the first balcony, waiting to buy a ticket to get to the top, waiting to get into the elevator to get to the top, waiting to take the picture, you want to take at the top and finally waiting for the elevators to get down again.
Of course, the view over Paris is magnificent but there are other places from which you can get an equally good and cheaper view over Paris (e.g. from the Arc de Triomphe, the Pantheon or Sacre-Coeur).
The whole Eiffel Tower journey took me around 5 hours (with the majority spend in queues) and cost around 17€ (12€ to get to the first balcony, another 5€ to get to the top). My recommendation would be to either visit the Eiffel Tower in the coldest Winter (assuming that their will be less tourists, but it will have felt -50C° on the top) or to just enjoy the Eiffel Tower and the Park behind it from the bottom. I have to admit that it was more impressive to stand right underneath the Tower (the Tower is massive, around 326m in height) than on top of it.