Here are some examples of Swedish dishes that I find tasty. Some, if not all of these might also exist in other parts of the world, but all of these dishes are in fact enjoyed here in Sweden. I also know that some of these dishes can be made in very different ways, so don't get mad if I miss some crucial ingredient in some of the descriptions. Enjoy!
Köttbullar - Swedish Meatballs
Perhaps one of the most well known Swedish dishes. The recipe may vary, the balls are usually made from minced pork, but you can also use beef, veal, lamb or whatever your heart desires. Other ingredients are eggs, salt, pepper, nutmeg and onions. The Swedish meatballs are usually served with boiled potatoes or mashed potatoes, lingonberries, gravy and pickled cucumber.
Recipe - http://damndelicious.net/2014/02/21/swedish-meatballs/
Pyttipanna - "Small pieces in a pan"
A dish which has many similar variation around the world (e.g Hash in USA,Bubble and squeak in England) the pyttipanna is made from dices potatoes, diced meat of any kind and onions. It's also common to add a fried egg on top. Usually served with pickled beetroots and ketchup. It's a perfect dish when you need to use up left-overs.
Recipe - http://honestcooking.com/pytt-i-panna-swedish-hash/
Gravad Lax - Cured Salmon
This dish i made from salmon, cured in salt, sugar and dill. Tasty both as an appetizer as well as on a sandwich. Usually served with Hovmästarsås (Lit. Head waiter sauce), a sweet sauce with dill and mustard.
Recipe - http://www.jamieoliver.com/recipes/fish-recipes/super-quick-salmon-gravadlax/
Kåldolmar - Cabbage rolls
A dish traditionally said to be brought to Sweden from Turkey by the Swedish king Charles XII. This dish consist of minced pork, salt, pepper and sometimes rice. This is then rolled into cabbage and baked in the oven. The rolls are then served with potatoes, gravy and lingonberries.
Recipe - http://www.food.com/recipe/swedish-cabbage-rolls-kaldolmar-108571
A lightly fried patty made from minced veal, egg, cream, salt and pepper. Usually served with mashed potatoes, peas and lingonberries. Named after district judge Marcus Wallenberg, who's father-in-law wrote cook books.
Recipe - http://honestcooking.com/swedish-wallenbergare-recipe/
Flygande Jakob - Flying Jakob
My personal favorite. Flying Jakob is a casserole made with chicken, chili sauce, cream, bananas and peanuts. You can also sprinkle some bacon on top, some people also ad Italian salad herbs to the mix. This is usually served with rice. The dish is named after its inventor Ove Jakobsson, who worked in the air freight industry, hence the name. This dish seems to be one that you either love or hate, some people removes the banana, but I consider this sacrilegious.
Isterband - "Lard ribbon? belt? (Yeah I know, a very unsexy name)
The isterband is a kind of sausage made from pork, potatoes and barley groats, it's very coarsely grounded and is smoked. There are regional differences to the isterband, perhaps the most famous is from the province of Småland. Isterband is often served with creamed potatoes in dill sauce and pickled beetroot.
Recipe - http://www.familyoven.com/recipe/swedish-lard-sausage-isterband/100429
Inlagd sill - Pickled herring
This is a classic dish served on most Swedish holidays, like Christmas, Easter and Midsommar. Herring is cured and pickled. In the pickling stage flavors are added, these can vary and new combinations are common. Usually peppercorns, raw onion and bay leaves are added, mustard and dill is also a sure bet.
Recipe - http://honest-food.net/2011/03/08/swedish-pickled-herring/
Smörgåstårta - Sandwich cake
This is a kind of cake, with several layers of white bread, between these layers are creamy filling, usually with mayonnaise, tuna, eggs or whatever you find tasty. The cake is topped with whatever you like, cold cuts, cured salmon, shrimps, vegetables, caviar and so on. The cake is served cold, often at parties.
Recipe - http://www.scandikitchen.co.uk/how-to-make-a-swedish-smorgastarta-sandwich-cake/
Ostkaka - Swedish cheesecake
This sweet dish is nothing like your regular cheesecake. Ostkaka is produced by adding rennet to milk and letting the casein coagulate. Other ingredients include eggs, cream and almonds. It has a very nutty taste, not too far from marzipan (But not so sweet). Ostkaka is served luke warm, often with jam and cream.
Recipe - https://recipereminiscing.wordpress.com/traditional-swedish-cheesecake/
Punchrullar - Punch-Rolls
Also known as Dammsugare (Vacuum cleaners). The story usually told is that these sweet pastries were made at the end of the shift when the confectioner swept the floor, took all the sweet crumbs and what not and made these tasty rolls, a good way to not waste anything for sure. This is of course not true for the Punch-rolls made today. The punch-rolls consists of crushed cookies, cacao, punsch liqueur and butter, this is rolled up in marzipan, with the ends dipped in chocolate. This is a classic to the swedish "fika"
Recipe - http://www.food.com/recipe/swedish-punsch-bars-95491