Sometimes, one can get "ruins fatigue." You see so many old rocks, barely-recognizable buildings, and crumbled statues that they all blend in to one another. This is not the case of the Aqueduct of Segovia. As you're walking to the city center, you see it peaking above the buildings and you get a tickle in your stomach and think "man, that thing is massive!"
Not only is it massive (around 6 storeys, I'd say), it's also in impeccable shape for being a 2,000 year old Roman monument. I'll leave it to the other recommendations on this page and the Segovia Tourism Bureau to tell you the full history of this archaeological wonder and UNESCO World Heritage Site, but I'll leave it at this: the Aqueduct of Segovia is, along with the Alhambra, one of the most amazing sights in Spain and the best-preserved and largest Roman ruin I've ever seen.