A week or two, we were told of changes in seating plans for our teams (a regular occurrence). I was talking to the boss and happened to blurt out that the actions of another woman in a cubicle close to mine were driving me to distraction.
I am so sorry Pakrat. I had a similar issue at one point, being a secretary, we listen to dictation from our attorneys and transcribe it into letters. We use headphones and that way no one else has to listen to it. The lady next to me was listening to it out loud, but with the headphones in her ears. I asked the boss to talk to her about it, but she refused, saying she had done it that way for years. But it was SO LOUD that I could not talk on the phone or listen to my own darn dictation. One day I finally lost it, stood up over the cubicle and said, can you actually USE the headphones, I cannot stand to hear that anymore? Turns out, she was such a moron that she could not figure out that she had it on speaker and had it turned up so loud because she could not hear it from the headphones. I cannot actually offer too much advice as I totally lost it and could have gotten in trouble for my response, but I understand your pain (at least some of it - waves her NT flag shyly) and I am so sorry!
Packrat - how horrible - I sympathise because even though I'm NT I find it hard to concentrate if there is lots of noise next to me. I think it perfectly reasonable to ask to be moved, however if it is impossible could you insulate your cubicle wall with something? Pin up a rug or some thick amterial (you can buy soundproofing material) to at least muffle it a bit. If you did that it might at least make her realise how much noise she is making.
Good luck
Pakrat
I'm sorry you are going through this, but I think you will need to put your own health before that of your boss as this problem isn't going to go away.
A woman of this sort is going to always think she's the the one who needs accommodating or can get away with whatever she does, she will also know that your boss doesn't like confrontation & will likely use it to get her own way.
I know some people think it is a minor thing
Pakrat-it isn't a minor thing for you if it is going to affect your health and your productivity at work..and I am sorry that you have to deal with this problem...
Your boss may not like confrontation-but he is the boss- He gets to have the problem by definition.
You could mention that you are sorry to have to bring it to his attention, again, as you are not a troublemaker-but that you are concerned about your health at work and perhaps there could be a happy solution to the problem..
I think you could mention to him again that you would be more productive if you had a quieter space-as in the past it hasn't really worked out being next to this woman.
Is there someone quieter you could be beside?
Are you able to 'trade' spaces with someone-or does the boss have to assign the cubicles, etc. ( not sure how it works)
GOOD LUCK!! Keep us posted 
Thanks for all your kind advice. I think much of the response at work to my issue boils down to "well, nobody else has said there is a problem so there isn't really one". It is not that there is a complete lack of sympathy - it's just not considered a serious enough issue to disrupt the team about (as somebody else would have to be swapped into her workpoint).
It's also as if it's "my perception" that there is a problematic level of noise. This in fact was the excuse used when I was sitting next to the same lady four years ago. The manager back then was trying to make out I was having auditory hallucinations in order to "prove" I was mentally ill.
My current manager would never do anything like that but I think he'd like to take a "wait and see approach" until the team is settled in a bit better.
On the bright side, she doesn't come in on Wednesdays, so I will have some respite.
I'm also going on holidays in roughly 3 weeks time and will be away for about 5 weeks visiting friends in Melbourne mainly.
My boss did a late April fool's day trick by saying we were going to get a rather unpopular manager for about two months while he was doing higher duties. I thought it was a trick so didn't get too perturbed but some others took it seriously and formed a delegation to go talk with him. About 10 minutes later, he told us he was staying.
The only thing about the other manager is she is rather a stickler for people being quiet so I might have got something done about the noise.
You might want to get some high quality headphones; they make huge ones that can totally block out all outside sound. At least don't use those terrible ear-killing ones that come with iPods. Although seeing as this topic is almost 2 months old I presume you've already done something about it.