Reed underwent offseason hip surgery and didn't practice during training camp or play in the preseason. The six-time Pro Bowl star missed four games last season because of hip problems after playing every game from 2006 to 2008.
"The competition to make our team was very heated, and we decided to keep a position player rather than a third quarterback," Ravens general manager Ozzie Newsome said in a statement released by the team. "We have a number of young guys who made our team who have tremendous upside, plus they can help us win this year. We've gone with two quarterbacks before."
"I had a couple of opportunities (in Baltimore), so now we'll just see what happens," Smith said. "If there is an opening somewhere else, we'll just take the bull by the horns at that time."
Cundiff prevailed in the duel with Graham, who was signed as a free agent in June after spending seven consecutive seasons with the Cincinnati Bengals.
"Congratulations to Billy. He won a great competition and he earned this spot," Ravens coach John Harbaugh said in the team-issued statement. "Both Billy and Shayne rose to the occasion and performed at high levels. We know Shayne will kick in the league, but we feel very good about the decision to go with Billy."
"I'm real excited. I'm more motivated than ever to prove myself," Jones said. "I can't wait to get to practice Monday. I want to show them they did the right thing by keeping me."
Another notable cut was wide receiver Demetrius Williams, a 2006 fourth-round pick who battled injuries for much of his four-year stay with the Ravens. He had 63 catches but just eight last season.
The Associated Press contributed to this report.