First of all, he said that to his disciples and only to us indirectly, if at all. He is speaking to the first-century church, and he makes the statement that the works they do will be greater than the works that he performed (John 14:12). Let me tell you what I don't think it means.
There are many today who believe that there are people running around this world right now who are performing greater miracles, performing miracles in greater abundance, and actually doing more incredible acts of divine healing than Jesus himself did. I can't think of any more serious delusion than that, that somebody would actually think they have exceeded Jesus in terms of the works he has done. There's nobody who comes close to the work that Jesus did.
THERE'S NOBODY WHO COMES CLOSE TO THE WORK THAT JESUS DID.
Some say that perhaps we can't do greater works than Jesus individually but that corporately we are able to exceed in power the things that Jesus did. We see amazing things happening in the first-century church through the power that Christ gave to his apostles. We see people raised from the dead through Peter and Paul. But at the same time I would challenge people by telling them to add up all of the miracles that, according to New Testament records, were wrought through the hands of Paul, Peter, and the rest of the disciples corporately, put them all together, and see if they measure a greater degree than those which our Lord performed. If Jesus meant that people would do greater miracles than he performed in the sense of displaying more power and more astonishing things than he did, then obviously one of the works that Jesus failed to perform was sound prophecy, because that just didn't happen. Nobody exceeded Jesus' works. That's what leads me to believe that's not what he meant. I think he's using the term "greater" in a different way.
I heard a church historian say that he was convinced that when Jesus made the statement "Greater works than these will you do," he was referring to the whole scope of the impact of Christ's people and his church on the world throughout history. I know a lot of people look at the history of Western civilization and say that the bulk of the church's influence has been negative—the black eye of the Crusades, the Galileo episode, and holy wars, etc. If you look at the record, you will see that it was the Christian church that spearheaded the abolition of slavery, the end of the Roman arena, the whole concept of education, the concept of charitable hospitals and orphanages, and a host of other humanitarian activities. I think, personally, that that's what Jesus meant when he talked about greater works.
"What did Jesus mean when he said we would do greater work than he did?" and other questions can be found in our Questions Answered section.