The Popes still use the first person plural. If you read the English translations of Papal documents, some of them are very good about using "We," "Us," "Our," and "Ourself," while others are not and use "I," "me," "my," and "myself." Curiously, if you look at the Latin originals, they are almost always in the first person plural. I attribute this to different... styles... in the Secretariat of State, which I believe is responsible for translations. The first time I read "Ourself," I was a bit confuzzled.
Usually in homilies nowadays the Pope will speak in the first person singular. But in rituals like creating cardinals and the Urbi et Orbi blessings, he speaks in the first person plural.
I am not sure where this has its historical groundings. By all means, I hope this is always retained into the future, but I have two theories as to its historical origin.
1) The Pope speaks with the entirety of his office, which includes not only himself, but also the authority of 264 other men with him.
2) It was common for important personages back in the day (and even somewhat nowadays) to use the first person plural.
I wager it is a combination of both.