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The following information is from John Dickson's The Christ Files, which is available as both a book and a DVD.
There are several early records which are thought by many historians to refer to Jesus. Here are three of the earliest. With only a sentence or two, sometimes the identifications aren't perfectly clear, and some of them are debated. As with Josephus, some people also argue that some records have been later tampered with by Christians, but as these ones are hostile to Christianity, that seems unlikely.
Mara ben Serapion, a Syrian stoic, wrote shortly after AD 73:
What advantage did the Jews gain from executing their wise king? It was just after that that their kingdom was abolished ... Nor did the wise king die altogether; he lived on in the teaching which he had given.
This is one of the less clear ones, but there are few alternative identifications than Jesus.
Tacitus, a Roman historian (AD 56-120), wrote in Annals 15.44:
Christians derived their name from a man called Christ, who, during the reign of Emperor Tiberius had been executed by sentence of the procurator Pontius Pilate. The deadly superstition, thus checked for the moment, broke out afresh not only in Judea, the first source of the evil, but also in the City of Rome, where all things hideous and shameful from every part of the world meet and become popular.
Pliny the Younger wrote in AD 110 to ask Emperor Trajan whether he should continue executing Christians. He said:
The sum total of their guilt or error was no more than the following. They had met regularly before dawn on a determined day, and sung antiphonally a hymn to Christ as to a god. They also took an oath not for any crime, but to keep from theft, robbery and adultery, and not to break any promise.
Upvote:3
A couple of other ancient references in addition to those mentioned by curiousdannii:
The Roman writer Seutonius, "The Twelve Caesars": "[Emperor Claudius] banished from Rome all the Jews, who were continually making disturbances at the instigation of one Christus." (This incident is mentioned in the Bible in Acts 18:2.)
There are also two references to Jesus by the Jewish writer Josephus. There is some dispute about the exact original text -- some claim that Christians edited Josephus to make it more pro-Christian, a question that could be debated at great length. Anyway, here's an English translation of the Arab translation of the original Greek: "At this time there was a wise man who was called jesus. His conduct was good and he was known to be virtuous. And many people from among the Jews and the other nations became his disciples. Pilate condemned him to be crucified and to die. But those who had become his disciples did not abandon his discipleships. They reported that he had appeared to them three days after his crucifixion, and that he was alive; accordingly he was perhaps the Messiah, concerning whom the prophets have recounted wonders."