Now, I am always slightly wary of bringing up the question of the historicity of the Resurrection except in answer to a direct question as it seems that everyone has their own definitions of the terms involved and there's often the danger being misunderstood. I am reminded of a theologian who used to preface his discourses on the Resurrection and post-Resurrection appearences with the disclaimer that if anyone understood him to be saying that it didn't happen, then they were misunderstanding him.
One of the keys with respect to historicity is the distinction between 'what actually happened' and 'how much of what actually happened is accessible to the techniques and method of the historical discipline'. (If I recall correctly, those Germans had the good sense to invent several words for history, each conveying a different shade of meaning.) As a unique and a priori wholly improbable event, it seems to me that from a secular point of view one cannot prove the Resurrection in the same way that one can prove that Napoleon was defeated at Waterloo.
That said, historical inquiry can deal with the events surrounding the Resurrection (the crucifixion, the empty tomb, the extraordinary claims of the disciples, etc...) to raise a huge question for the secular enquirer regarding what happened. Either there was a most extraordinary hoax or it was as the Apostles claimed. Further than that, one can only (fruitlessly) argue the probabilites of each scenario. For the believer, such a historical investigation at least provides the neccessary historical possiblity for belief. (It's always worth bearing in mind that ultimately it is grace that makes it possible to have faith in the Resurrection.)
It is, of course, the case that very few (if any) of us make our initial approach to this question in the historical manner. We are normally brought up in a particular tradition of faith (or lack thereof). We access the event of the Resurection through our own religious and ecclesial experiences. How this works in practice does vary - some by experience learn to accept the Church as a reliable witness. Others experience the power of grace in the sacraments or through particular individual experiences. This is why I was interested to note that one of the commentators at Pontifications quotes from 1 John 5:
7 For there are three that testify:
8 the Spirit, the water and the blood; and the three are in agreement.
9 We accept man’s testimony, but God’s testimony is greater because it is the testimony of God, which he has given about his Son.
10 Anyone who believes in the Son of God has this testimony in his heart. Anyone who does not believe God has made him out to be a liar, because he has not believed the testimony God has given about his Son.
11 And this is the testimony: God has given us eternal life, and this life is in his Son.
12 He who has the Son has life; he who does not have the Son of God does not have life.
So, it seems to me that there is certainly a historical case to be made, (and the Catholic intellectual tradition makes it particularly appropriate that this case be made) but that faith is not the endpoint of a chain of historical scientific reasoning, but also demands grace. The more important aspect therefore is the salvific power of the Resurrection. (As an aside, one could imagine, for example, someone who investigating the issue convinced himself that Jesus did rise from the dead, but perversely held that this didn't have any consequences for himself personally. This I would not count as faith.) It is an awareness of this salvific power which brings us to belief.
Of course, it is not always easy to seperate the historical and non-historical aspects when looking at these issues. One of the arguments in favour of something extraordinary happening after the death of Christ is the incredibly transformation of a dejected group of Apostles into a missionary church which spread throught the Roman Empire. Is this historical evidence for a miracle or an example of grace at work? (I don't say the two exclude each other.)
One could go on to discuss the nature of the appearances of Christ and issues such as why the death and Resurrection of Christ is salvific. (From a Catholic point of view it is interesting to note that there is probably less definitive dogma regarding why the Cross and Resurrection are salvific than one might expect.) But it's getting late, so maybe that's a discussion for another day.
[Edited to add:
Also in a similar vein is this post dealing with the centrality of the Resurrection to the earliest Christian proclaimation.]