Growing up in a Danish household, pickled beets were always abundant, but particularly so at Christmas time. It is usually the first thing I make as Christmas gets close.  Then I start in on the cookies and goodies.
We would have pickled beets with everything, but most commonly on open faced rye bread sandwiches with cheese, pate, and sausage meats.  I think pickled beets are a main event like Cranberry sauce is to most other people.  All of my sisters to this day make this recipe.  One year I can't remember why, but I did not make them.  I still hear about it from my daughter, in fact she actually asked me to make them for her birthday!
The original recipe will follow, but I wanted to mention, this recipe can also be made with Apple Cider Vinegar, although, you do get quite a different flavor.
This makes a fair bit of seasoned vinegar, actually I had 2 cups leftover, which I refrigerated to make more pickled beets another day.
6-8 large beets
3 cups white vinegar
2 cups of warm water
2 1/4 cups sugar
2 Dashes of:
mustard seed, celery seed
good pinch of ground cloves
3/4 tsp. salt
Wash the beets well, leaving on the skin, tops and bottoms.  Place into a large pot, cover with water and bring to a boil.  Cover with a lid, turn down to simmer and cook until tender.  Mine took 1 1/2 hours to cook through.
Meanwhile sterilize your jars and lids.  In another pot, combine the water and sugar. Keep stirring until all of the sugar is dissolved.  Then add the vinegar, and seasonings, stir to combine and set aside.

When your beets are cooked, drain the water off, remove beets to a platter to cool. I line my cutting board with parchment paper to prevent the beets from staining the board.  (I care more about staining my cutting board than I do my hands) Once cool, cut the tops and bottoms off, then peel the beets, slice in half, and then into quarters.  Slice the beet fairly thin, think of a slice on top of a sandwich.
Fill your jars to the top with the sliced beets, then using a ladle pour on the seasoned vinegar, covering all of the beets. Cover with the lids, and refrigerate.  They taste their best after about 3 days and will keep for ages in the fridge.