What are the usual rules for tipping in Denmark? I'm especially interested in:
- Other places I had no idea people usually tip?
That's easy: Tipping simply doesn't happen in Denmark.
All of the places you list have posted prices that include all applicable taxes and enough profit to pay the entire staff full wages.
(One example: It is common for credit-card terminals in taxis to allow you to enter a tip amount before you key in your PIN. However 19 times out of 20 the driver will push the "cancel tip" button himself before he even gives you the keypad. Some drivers may opportunistically hope for tips from passengers who're obviously tourists and may not be aware of local customs, but it's neither normal nor expected).
To slightly disagree with Henning Markholms answer, being a fellow dane.
Tips will not be frowned upon, but are definitely not expected and you would not incur any dirty looks for not tipping. The tipping line is rarely used when paying with credit cards, in some cases it is actually extra work for the server, as he or she will have to get a new receipt for you. If you really want to tip, leave a few coins (the largest danish coin is about USD 3-4).
Some bars will have a large glass on the counter for tips. But nothing is expected.
When paying your hotel bill you never tip. If you buy drinks in the hotel bar, you could tip, but it is not expected.
If you pay cash in a taxi you might find that the driver could be very slow to find the last few coins of your change. Don't worry about that, they give up quickly and find the coins, they just want you to have time to say something like "don't worry".
The only exception I could think of where you might be pressured to tip would be strip clubs or the like. But don't go to places like that unless you really want to waste a few thousand kroner.
In addition to the other answers: As Bent already stated, it's sometimes extra work for the server to handle a tip, especially if you're paying with a card (which, by the way, is much more common than paying with cash in Denmark). To avoid the extra hassle, many restaurants give you the bill in a small basket/small plate/something that could just be considered decorative. If you feel like leaving a tip after you've paid the bill, it's easy to drop a few coins in the basket/plate right before you leave and not make a fuss about the tip. The waiter will pick up the tip when he/she clears the table afterwards.
You'll also be spared the, for some, embarrassing feeling of confronting a waiter who sees your tip.
This way you can pay the bill, and drop a few coins before you leave and avoid all feelings of guilt associated with leaving no tip/tipping too little.