Below I have described the places and things I saw on what was my third visit to Paris (I had visited previously in September of 2006 and September of 2008, so not all of Paris' must-see sights will be listed in this entry).
Eiffel Tower: Even on my third visit to Paris, I made sure to fit in several stops to see the gorgeous Eiffel Tower. I recommend seeing the tower during the day and at night. There is nothing more beautiful than when the tower is lit-up during the evening hours, especially when the light show comes on at the top of each hour for several minutes. I find it truly mesmerizing and worthy of all the hype it receives; I will never tire of this tower! I have only gone up into the tower once, and that was probably enough for me. I have found that there are other areas in Paris that provide a better view of the city (i.e. Arc d'Triomphe, Sacre-Coeur, etc).
Notre Dame Cathedral: This 700 year-old cathedral is one of Paris' many must-see sights. Like the Eiffel Tower, I also recommend visiting during the day and at night. While the church itself is free to enter, it does cost extra to tour the treasury and to climb the tower (the latter I highly recommend). I climbed to the top of Notre Dame on my first visit to Paris and to this day it's still one of my most favorite moments I've had in the city. The view from the top is great and being up-close to the gargoyles is quite awesome!