Although I've covered the statues looted from the Hippodrome in Constantinople here, others survived into the Ottoman period.
A 5.35 m high bronze column originally stood in the sanctuary at Delphi, where the Serpent Column had been dedicated by the Greeks to celebrate their victory over the Persians at Plataea in 479 BC. It had originally been topped by a gold tripod, but that was looted by the Phocians in 355 BC (Pausanias X.13.9).
It was presumably brought to the Hippodrome by Constantine, and continues to be there to this day. I was always under the impression that the snake heads were knocked off during the Fourth Crusade in 1204, but they were clearly still intact when this scene from the Surname-i Vehbi was painted in 1582.
Another surviving monument is the base of Theodosius under the Obelisk
The Greek inscription on the west face says that the Obelisk was erected in 32 days.
The Latin inscription on the East face is heavily damaged, but records that the obelisk was raised under the direction of Proclus the governor of Constantinople in "three times ten days" ... (I guess they were hoping no-one noticed the two missing days ...)
The model is the latest reconstruction by the archaeologists and curators at the Topkapi:
sculptures from the Hippodrome were lost long ago, we know that there were seven statues of the charioteer Porphyrios on the spina. Two of the bases survive and are now in the Archaeological Museum.