Some who gathered Saturday night brought candles, while others held up their smartphones to take photos of the scene. The mood was somber, with no chanting or shouting.
Paterno's doctors say his condition has become "serious" after he experienced complications from lung cancer in recent days.
Paterno's son Jay tweeted, "Drove by students at the Joe statue. Just told my Dad about all the love & support--inspiring him."
The statue is just outside a gate at Beaver Stadium.