Yes it is possible.
A few websites will insist that the "point of sale" to be in the country where the first flight originates. So if you are searching for flights from Dubai from the .co.uk website, suddenly everything is priced in AED. Iberia.com certainly used to insist on this, but they seem to changed practise recently. British Airways does do it on their website, but you can just call them instead.
Other carriers' websites (such as LAN Chile) will simply accept your choice of website to use and sell from their office in that country. [Often with big (>50%) savings if you visit their Chilean website.]
expedia.com.hk sells flights from Hong Kong availability wherever the ticket begins [and there was recently an industry-wide fuel surcharge miscomputation in Hong Kong which was of some benefit to those who knew it], in which case I would imagine it applies for the majority of the Expedia franchises.
With British Airways you can create a reservation at any BA ticketing desk (sold out of local availability at local pricing) and then pay in your local currency later by phoning your local office, although there is a phone fee it can be waived if you ask nicely. The help desk will also honour requests to look from other points of sale, at least within Europe.
Distinguishing on point of sale is now illegal within the European Community although a few major airlines (AF, BA) continue to do it. (See EC 1008/2008 Article 23(2).)
For a while it was possible to avoid credit card fees on Air France by buying from the Irish version of their website.
There are some disadvantages to this practise:
The contract is considered formed in the point-of-sale country, so the laws of that country will apply to the transaction. That's probably only going to be important if you need to do a charge back or rely on some local consumer protection later.
If your credit card applies any forex fees or spread in the transaction, remember the transaction is by default denoted in the selling office's currency.
Some cheap domestic-only fares (especially in South America) actually have residency requirements. Check carefully if this applies. I've only ever seen this in South America though.
A small number of providers will not honour payments from a foreign credit card. You can sometimes bypass this by "accidentally" choosing the wrong country when you enter your billing address (American Express for example doesn't actually verify the billing country is correct). Alternatively your bank may decline the transaction as a counter-fraud measure if the transaction is out-of-character for you.