Hi everyone. I think the ticket I've booked is accidentally 91 days (9 oct-7 jan). I think the 7th Jan is the 91st day- how are the days calculated? I'm presuming the day I arrive and the day I leave are both calculated? I don't want to mess around with US immigration- is the only solution to change my ticket (which will cost £100)? Thanks so much!
Assuming for a brief moment that your enquiry is genuine, I think you're fine. The day of arrival is the zeroeth day, and in your case, the 90th day is 7 January.

Assuming you don't know how to calculate using the Julian calendar (I did that to find the time between dates when I wrote computer programs but that was decades ago and I couldn't do it now), you can find lots of Web sites that do the same thing by doing a search on calculate time between dates. Voila. The elapsed time would be 90 days.; http://www.timeanddate.com/date/durationresult.html?d1=09&m1=10&y1=2013&d2=07&m2=01&y2=2014

Thanks for your help! That calendar says its 90 days not including the end date though- that's what I was worried about. Does that not count?

I don't know what countries' passport you are carrying (U.K. since you mention pounds?).
I do know though from research about the crazy visa system we have in the U.S. to help let foreign friends know what to expect when visiting that even in visa waiver countries the "allowed length of stay" is established upon arrival and not set in stone. I've seen 60- 90- and 120-day allowances given to friends who have visited.
My suggestion is to show the INS officer your return airline ticket upon arrival. If your allowed length of stay is not sufficient they will most likely tell you to change your ticket.

NO it is a common misconception that the first day is not included. We've discussed this earlier in this thread and I presented proof that both first/last day are included, so you get 89/90 days depending on how you count it. Here is picture proof again. Take a look at your passport Ian and you should see the same for your last visit.
Please see the thread above for an in depth discussion about this exact question and ideas to get around it. In short, I would NOT attempt to enter the US for 91 days. There is a small risk you won't even be allowed to board your plane in Europe.
Oh, and it is nonsense that you can get 120 days on a visa waiver.
Mad Max ... I think you're right.
We entered on 5 May (Day 1) and our visa stamp says we must leave by 2 August, which is 90 days according to Excel. So - the arrival day and the departure day are counted in the 90 days. Maybe the OP does have an arithmetical problem.