These are the dishes I was served as a kid. Not all are strictly Danish in origin, but most are eaten regularly by Danes. Many of these are based around fish and/or potatoes. You can also look at Nordic Recipes for related dishes.

Breakfast:

• Havregrød (Oat Porridge)
• Øllebrød (Lit. Beer-bread. A kind of porridge)
• Wienerbrød (Lit. Viennese Bread, Danish Pastry)

Lunch/Smörgåsbord:

Smörgåsbord (buttered bread table) is actually the Swedish name for it. In Denmark, we call it Smørrebrød (buttered bread) or Det store kolde bord.

• Franskbrød (French Bread)
• Italiensk Salat (Italian Salad)
• Karrysalat (Curry Salad)
• Leverpostej (Liver-paté)
• Marinerede Sild (Marinated Herring)
• Mayonnaise
• Remoulade
• Russisk Salat (Russian Salad)
• Spegepølse (Salami)
• Spegesild (Salt Herring)
• Surdejsrugbrød (Sourdough ryebread)
• Torskerogn (Codroe)

Dinner:

• Biksemad (Similar to Hash)
• Blodpølse (Blood sausage)
• Boller i Karry (Curry-Lumps)
• Brasede Kartofler (Fried Potatoes)
• Brune Kartofler (Caramelled Potatoes, thanks to andersa)
• Brun sovs (Brown Sauce)
• Flæskesteg (Roast Pork, thanks to andersa)
• Forloren Hare (Fake Hare)
• Forloren Skildpadde (Fake Turtle, thanks to nocte)
• Frikadeller ("Danish Meatballs", thanks to andersa)
• Gule Ærter (Split Peas)
• Gullash (Goulash)
• Hakkebøf (Chopped Beef)
• Kartoffelmos (Mashed Potatoes)
• Kogt Torsk (Boiled Codfish)
• Labskovs (Lobscouse/Stew)
• Medisterpølse (Spiced Sausage)
• Kartoffelsalat (Potato Salad)
• Plukfisk (Stewed Codfish)
• Risotto
• Rødkål (Red cabbage, thanks to andersa)
• Spejlæg (Fried Eggs)
• Stuvede Kartofler (Potato-White sauce)
• Sylte (Brawn/Headcheese)

Cake/Dessert:

• Brunsviger (Braunschweiger, thanks to andersa)
• Kærnemælkskoldskål (Buttermilk Cold Bowl)
• Lagkage (Layer-Cake)
• Pandekager (Pancakes)
• Ris à la Mande (Rice with Almond, thanks to liveforever)
• Rødgrød med Fløde ("Red Porridge with Cream")
• Æbleskiver (Applecakes/appleslices, thanks to Jacob-r)

Note: If a link lacks a writeup, ask me, and I will change my priorities accordingly... The wupped dishes are bold.

Sources are my mother's cookbooks.
Feel free to /msg me if you know of more dishes.