That's fun ! Although "most associated" does not mean "representative"...
I'd say for France, it has to be Opinel, which is still a very popular knife (every worker has one in its toolbox or car trunk, it's the go to beater that does the job and doesn't worry you in the least about being damaged or lost). Laguiole is of course the upper range contender here, it's the better knife you get when you are into knives. However, the pattern with the longest history of being popular throughout all social classes (peasants, workers, sailors...) would be the Pradel (created in the 17th century and wildly copied and replicated by all cutlers to the point that the original creator (Pradel) never benefited much from its own design). And hey, the Douk-Douk was an entry level knife designed for the French colonies (understand "trade knife"). While it became famous as a guerilla weapon in North Africa, it still is, and has always been, a French production (cutlery Cognet).
Corsica : has its own very attractive patterns. The "iconic" one is the Vendetta. I prefer the Curnicciolu, the shepherds' knife.
Now let's proceed with my neighbours :
UK : the Fairbairn-Sykes commando dagger pops out, although England has a very rich cutlery tradition.
Spain : Navaja (because it's iconic). I cannot think navaja without thinking Spain. And it inspired so many French knives (including the famous Laguiole).
Italy : many regional patterns, all elegant and functional. The stiletto switchblade has earned its place through movies and great popularity in the 50's, so yes. I will choose the Resolza : although it's a Sardinian pattern, it combines simplicity, functionality and elegance. That's my vote.
Germany : the Jagdknicker is the most specific pattern I know but the Otter Mercator K55 had its frenzy back in the days, so it certainly deserves to be close second.
Scotland : the Sgian Dubh. The pattern has been spoiled by Victorian folklore but can still be found in useable renditions.
Austria : the Taschenfeitel. A small, cheap knife (cheaper than the Opinel, imagine !) but it does cut and weighs nothing.
Sweden : the Classic Mora just springs to mind.
Finland : the Puukko.
The Saami nation (spread over the north of Norway, Sweden and Finland) : the Leuku. A big, very special knife, but they use it for almost everything.
The not so close neighbours :
USA : Bowie, of course, but also the Buck folder.
Brazil : the sabre machete.
Malaysia : the Parang (a very interesting crossbreed of short chopper and machete). Similar to the Golok (look up Martindale Army Golok Machete). In the "iconic" department, the Kriss, of course.
Australia : Huge Crocodile Dundee Bowie ("that's not a knoife, this is a knoife !").
Japan : Higonokami and Tanto, but it's hard not to mention their kichen knives, especially the Santoku and the Gyuto.
China : the Chinese vegetable knife, the Cai Dao. Fantastic kichen knife that does it all brilliantly (you will only need to add a small knife to peel garlic and debone meat. I'm still amazed by the Cai Dao...).
