I haven't come across any American divers in the flesh so I cannot speak from experience about them. In Europe though, there are certain common opinions about divers of certain nationalities. There was a thread on a British diving forum recently on the subject of diving stereotypes; I cannot find it now but I'm guessing it was pulled as it was teetering on the edge of xenophobic within a few posts.
There is a certain arrogance that is common amongst British divers that we are the best in the world. In some respects I agree as the hardcore UK divers are aclimatised to diving in cold water, strong current and poor visibility. This however could be said of people from countries such as Norway where they also have to deal with these conditions.
You also get the UK divers that only ever dive when they go abroad so theoretically they will be the same as any holiday diver. I was talking to a lad on the train recently. I was reading 'Deco for Divers' by Mark Powell and he struck up a conversation about it, telling me he was an 'advanced diver'. The British Sub-aqua Club (BSAC) award a certification by this name. An advanced diver by their standards is somebody who can plan expeditions, lead groups of divers and have excellent seamanship skills. I suspected (and soon confirmed) this lad was a PADI AOW. He asked me what the book was about and he then asked what decompression was!
Another time I was helping out on a rescue diver course. There was a young British couple on the course and this was their first ever dive in the UK. When the instructor started rounding everyone up, she said she hadn't set her kit up (the instructor had asked everybody to get kitting up quite a while earlier). She complained he had not helped her put her kit together, and was almost in tears as he told her in the gentlest terms we were not on a Red Sea liveaboard and RD candidates were expected to know how to set their kit up.
The group of divers that seem to have the worst reputation is the Russians. In recent years, there has been a massive surge in Russians visiting European holiday resorts and a lot of them are diving. We use a dive centre in Malta for an annual club trip. The owner is English and has a couple more Brits working with him along with a Polish girl and an Austrian lad. Most his clientele are British but the Polish and Austrian instuctors are both multi-lingual, so he gets a few German, Dutch, Austrian, Polish etc. diving with them. The year before last, one of the instructors was filling out the dive log. When she asked one of he lads for his air out, he decided to have a bit of fun with her and replied "Ten bar!". She looked at him with a worried look and he burst out laughing as he showed her his SPG that showed fifty. The Austrian lad smiled and said "I think maybe you like the Russian way of diving? Every Russian dive finishes with a CESA!".
The owner of the dive centre says he will not take Russians. He said he doesn't refuse to take them, but usually recommends they use the place around the corner as they have a couple of Russian speaking staff. This year he took us to the marina for a boat dive. We were surprised to see a wreck of a boat on our jetty with a load of others on board. I was surprised as I expected a better boat, and I expected we'd have it to ourselves. The owner of the dive centre told us to wait until they got off. There were collective sighs of relief and he said, "Russians! Stay well clear of them!". The boat left, with barely a square inch of space to move on the deck and seawater practically coming over the gunwales. The owner of our dive centre shouted as our boat moored up, "Right guys! Let's get on quick! Make sure you've not left anything in the vans! First stop, we dive the statue of Christ and the Imperial Eagle. Then back aboard, a bit of a cruise around, a bit of sunshine, a bite to eat and then we'll find out where those Russians made their mayday call and go and dive that!".