The viewing, at the Pasquerilla Spiritual Center on the Penn State campus, was open to the public during the afternoon.
The line of those waiting to get in stretched more than a quarter-mile across campus, causing waiting times of at least 2 1/2 hours for most in frigid January temperatures.
During the morning the Paterno family held a private service.
The current Nittany Lions football team, led in by new head coach Bill O'Brien, was the first group at the viewing.
"It's been a very sad couple of days here in State College, and really in Pennsylvania and the state of college football," O'Brien said. "It was really important for me to lead our team over to the viewing of Coach Paterno and greet his family."
O'Brien escorted his team off the three blue Penn State buses that carried Paterno's teams to Beaver Stadium each Saturday in the fall.
Following the current squad, more than 500 former lettermen paid respects to their former coach.
"It was such an opportunity to be around a person who possesses the kind of wisdom and knowledge [Paterno] had," former All-American linebacker LaVar Arrington said. "I was one of the few who had the opportunity to know the man. It was a very sobering day."
Arrington was among many former Penn State stars who attended the viewing, including Franco Harris, John Cappelletti, Kerry Collins, Larry Johnson Jr. and Daryll Clark.
Former Penn State assistant coach Mike McQueary, who testified in a grand-jury investigation that eventually led to child-sex-abuse charges being filed against former Penn State defensive coordinator Jerry Sandusky, was also among the mourners.
"He was everything to you, next to your father, wife, mother," McQueary told the Daily Collegian, Penn State's student newspaper. "He was everything you would ever want in a head coach or a university icon."
"It was a little bit of sadness, but I think it was more rejoicing in the fact that we were able to be in the presence of somebody who was so great," said Johnson, a Doak Walker Award winner in 2002. "There are a lot of players that he's coached from generations and generations, but we never thought we'd be a part of what Joe Paterno was, and who he was, and how he carried himself, how he carried his business. I was a part of history."
In recent months Paterno's legacy at Penn State has been called into question because of the ongoing Sandusky case. But Paterno's former players defended him passionately yesterday.
"I hope it will be the same legacy he left in every one of us, and that's a tremendous man, a tremendous mentor and a tremendous leader," former tight end Kyle Brady said. "That's what we know him as. That's the essence of Joe, the real Joe, and in spite of what's happened these last months, I sincerely hope that's how he'll be remembered."
Another public viewing service was to be held today at the Pasquerilla Spiritual Center from 8 a.m. to noon, followed by a private funeral service at 2 p.m.
Tomorrow, a public memorial service - titled "A Memorial for Joe" - will be held at 2 p.m. in the Bryce Jordan Center. Free tickets for the event, to be held at the nearly 16,000-seat arena, ran out in minutes yesterday morning, Penn State spokesman Jeff Nelson said.
Nelson said Beaver Stadium, which holds more than 100,000, was not an option because of the weather.
"We feel bad about that," Nelson said. "But when you have as many fans who loved Joe Paterno as there are, there's just no way we could accommodate everyone."
For those who won't be able to attend tomorrow's memorial service, yesterday provided one last chance to pay tribute to Paterno.
Mary Fowler of Bedford, Pa., who went to high school with Paterno's wife, Sue, in Latrobe, Pa., endured the cold weather and long lines.
Like many of the lettermen, she remembers Paterno for his positive contributions to the university.
"When you say Penn State, you don't say Penn State. You say Joe Paterno," Fowler said. "He'll never be forgotten, not ever be forgotten."