I went to the Eiffel Tower web site looking to buy tickets for an upcoming visit, and found that, except for a few days, it is sold out for basically two months. I am guessing that it is not truly sold out because a friend was recently in Paris and said he was able to walk up and buy tickets on the spot. Of course, he was visiting it at night on a weekday. I'll be visiting in the daytime on a weekend. Does anyone have any suggestions for alternative sources of tickets, or recommendations for when to arrive to have a chance of buying tickets on the day of the visit?
Update: Read my answer below for my experiences visiting the Eiffel Tower.