Ireland national dish
I'll pretty much second everything that Theresa said about Ireland. Although I've been going there for 15 years and I don't think I've ever seen coddle...
Ireland is more about the quality of the ingredients than the actual dishes. In recent years there's been a trend for the higher-end places to really concentrate on getting the best ingredients and cooking in (I think) more of a French style, or at least improving on traditional Irish recipes.
Definitely get black (and white) pudding, sausages, rashers, brown bread (always served with some of the best butter in the world), smoked salmon (not as salty as NY lox).
The best bacon and cabbage is awesome, but more often than not, I'm dissappointed with it and the blandness of "parsley sauce."
If you see a pub advertising a "carvery lunch," go for it. Nothing culinarily overwhelming, but very typical and real Irish comfort food. I highly recommend it paired with a pint of Guinness.
If you're hungry after a night at the pub, go to a chipper and get chips with salt and vinegar.
I just returned from a two-week vacation in Ireland and loved the bacon and cabbage. I would like to make this at home here in Canada but am not sure which cut of meat to ask the butcher for. Unfortunately I don't know of any Irish butcher shops here in Toronto so any help would be greatly appreciated.
You don't necessarily need an Irish butcher to get the right cut, but terminology temds to be different across the globe. If I was serving bacon and cabbage, I would buy any cut that is ok to boil and/or roast - so ask your butcher.
I boil a piece of ham/bacon (here I would use shoulder or gammon) for half the cooking time and then roast it with a mustard, honey and molasses/brown sugar glaze for the rest of the time, and that seems to work.
Green cabbage is traditional, but sweating finely chopped onions with finely chopped white cabbage is delicious. Also, make sure you use plenty of parsley in the white sauce - flat leaf has more flavour, but lots of very fresh curly parsley can also do the job. It helps to infuse the milk with a bay leaf or two and some raw onion and black pepper corns to give it more flavour.
Two Irish dishes worth trying are potato-based. Boxty is a potato pancake of sorts. Champ is a mashed potato dish.
If you can find good fish & chips in either Ireland or Scotland, you should enjoy them.
I have vacationed in Scotland far the past several years and have had excellent shellfish (mussels, scallops, langoustines, etc.) there. Unfortunately, most of the seafood sourced from Scotland gets shipped to France, Spain, etc. right off the boat.
You could probably argue that the national dish of Ireland is Irish stew - a lamb stew cooked with potatoes. It will turn up as pub food, but is often not particularly good so I wouldn't get your hopes up.
Coddle, mentioned upthread, is very Dublin-specific, and is again I think the kind of thing that tends to taste better home-cooked than when treated as cheap pub stodge.
Don't miss soda bread though (white or wholemeal - good with smoked salmon), and potato bread, and I second the vote for seafood if you're in a coastal area. If you're staying in a B&B, the cooked breakfasts will almost certainly be good. Try black pudding and white pudding if they're on offer (Clonakilty black pudding is particularly good).
Local cheeses can also be very good, but specialist delis or restaurants which actually stock them can be harder to find.
One other thing to look out for in Scotland at this time of year is that the raspberries are some of the best in the world. Just buy a punnet and try them.
I forgot to mention Scottish national dishes. Again, these are only good if done properly and generally not so good in the more touristy places.
Cullen skink is a lovely smoked fish and cream soup
Arbroath smokies - hot smoked haddock
Smoked Salmon - arguably the best in the world
Often regional foods in Scotland and Ireland are more about locally sourced produce, as opposed to actual national dishes - so fish, seafood and game are big in Scotland, and as you can see, smoked fish in particular. Fish and seafood are also common around coastal areas of Ireland. And sausages in Ireland can be very good too - as always, though, depending on the supplier.
Many years ago I had an Irish boyfriend, and his mother used to make what they called "coddle" every saturday lunchtime - it was basically whole sausages cooked for ages in stock, onions and tomatoes (I think). Once it was cooked, she'd take it off the heat, but leave it for her large family to help themselves to and reheat when they came in from work or the pub at any time of day or night. It doesn't sound very good, but it tasted great - particularly after a few pints. And best eaten with good crusty bread.
One thing to consider is that national dishes are often disappointing if not eaten at home or in the right place/atmosphere.
Having said that, I know nothing of food from Germany or Norway, but the two Irish national dishes I know of are Irish stew and boiled bacon/ham with cabbage, spuds and parsley sauce.