I've given this more thought over the last few days, and spoke to a few people from different backgrounds. My original answer was flawed, and I'd like to take another crack at this.
The short answer is "We don't know for sure." The original Greek recorded as Jesus' words is "gennema ampelos", which means "fruit of the vine." This can be taken to mean either fermented or unfermented grape juice.
This topic is the matter of quite a bit of debate, and any answer you get other than "we're not sure" (including my original) is going to be based on conjecture, logic based on un-provable assumptions, and bias, rather that provable fact. (Assuming that "provable fact" on this site would include a clear Biblical statement on the matter.)
My original statement included my opinion that this is really a non-issue. it is a non-issue for me, but in speaking with several friends from different backgrounds. (Baptist, Catholic, Evangelical free, and Lutheran) over the last few days, I've seen that it's important to them
for other reasons.
In the "non-alcoholic" camp the issue seems to center around whether or not drinking is allowed for a Christian at all. The bias is that drinking is an outright sin, and since Jesus was sinless, then it couldn't have been alcoholic. If it were, then Jesus was a sinner. For that camp, there is no compromise.
In the "alcoholic" camp, I was surprised to find that the issue was a matter of credibility of Church authority. More than a few of the people I talked to stated (and I don't know if this is true, I just know what they told me) that their Church taught that it's alcoholic, and that they believed the Church. When pressed, one of them got really irate and said "Are you calling the Pope a liar?" Now I don't know what the Pope says about this, not being Catholic myself, but clearly this issue for her was a matter of importance. Believing otherwise would undermine her rock-solid faith in the Catholic Church and the authority of the Pope.
I can't stress enough here that I am not saying that the Pope or the Catholic church says anything on the subject. I really don't know. I'm relating her experience to illustrate a point.
Based on the fact that the original Greek is unclear, and the arguments on either side are based on un-provable assumptions and bias, my final answer is still "We don't know for sure."
I personally still think that it was unfermented, but I wouldn't state dogmatically that it's unfermented.