Here are some of the things I look for myself when I travel, and a list of links that you might find useful when you visit Copenhagen. This page is a work in progress, stay tuned for more. In case you check back once in a while, I have marked recent additions in yellow. (Inspected for expired links and updated as of January 2016, wow, that is a never ending job!)

Copenhagen Airport (Kastrup)
Transport by Metro (a 20 min. trip to the centre)
Or you can take the train (see under Transport)

Bicycles for rent:
Rent a Bike
Donkey Bike  NEW

Bicycle taxi's and rickshaws (sigthseeing and for just getting around):
Parked around the busy places in Copenhagen, but you can also book them in advance.
Copenhagen Rickshaw (in Danish only)
Flying Tigers

Bike share / public bikes:
After retiring the clumsy but oddly missed free bike program, the city recently launched the new bike share Bycyklen. I have not testet one yet (not looking forward to it either, as they weigh 20 kilos, and for that reason come with electric assistance), but you can read about them here: Bycyklen.

Once you are on the bike:
Copenhagen Bike Tours (GPS guided bike tours)
Cycle Guide DK (online bicycle guide, including the all important hand-signals)
The rules and fines, don't be the cashcow.. (article in English from Cph Post listing rules/fines)

Bring your bike on the train:
You can bring your bike for free on the train (but not the Metro, that one still takes a special ticket), except on Nørreport Station in the rush hour, and in the case where there is no space left (the conductor will let you know). And you must place your bike in the bike cars, look for the bike symbol on the doors.

Cash vs. credit:
The currency here is Krone (DKR/Danish Crowns)
Paying with foreign cards often comes with a transaction fee on top, and the smaller shops and restaurants may not accept your brand of plastic. The Danes pay with Dankort, which is really a debit card.

Currency exchange points vs. banks: 
Avoid the currency exchange places on the pedestrian street like the plague, they are basically out to suck you dry, with poor exchange rates, high fees and all kinds of hidden costs. The banks have slightly better exchange rates (on the day I checked),  but you can not always count on the banks to be open when you need them. The opening hours for banks are Monday through Wednesday plus Friday until 4PM, Thursday until 5PM and weekends closed.

Freetown Christiania on Christianshavn, download pdf guide in English from this page.

City guides:
Architecture City Guide: Copenhagen 
Anywho (shop guide, fashion bloggers picks) 
CPH Treasures (guide to second hand, thrift and vintage stores in Copenhagen) 
DAC / Danish Architecture Centre (architectural guide)
Guide to Copenhagen
In & Out Guide (events)
Kopenhagen (listing all contemporary art shows/openings, in Danish only)
MIMOA (not Danish, but listing interesting architecture in Cph., w. surprises even to locals)
Weirdwalks (alternative guided tours of different themes. Haven't tried it, but it sounds fun) 
Yelp.dk (recently launched user review site, in Danish but w. some reviews in English too) 

And, if you are in the mood to get to know us better:
Denmark.dk (the official website of Denmark, in English/German/French/Spanish) 

Danish online news in English
DR (Danish TV and radio, online news in English)
The Copenhagen Post (newspaper)
The Local, DK edition  

Electrical current: 230V
For detailed electric plug info check What Plug, ancient but really informative site. (eg. US to DK)

Emergency numbers (only):
Emergency: 112
Police: 114

Gay life:
Copenhagen Gay Life (gay city guide)
Copenhagen Pride (gay city guide/parade is only once a year, but there is lots of info) 
Out & About (gay guide)

Internet access:
More and more hotels, bars, cafés and some buses and trains now offer customers free Wi-Fi.

Music venues:
Amager Bio (Amager)
Culture-Box (Centre)
Jazzhouse (Centre)
Huset Magstræde (Centre)
Jazzhus Montmartre (Centre)
Rust (Nørrebro)
Stengade (Nørrebro)
Vega (Vesterbro)

+ The Visit Copenhagen's guide to Cph Nightlife

Just to name a few.

Opening hours:

For small shops (most shops, really):
Monday-Thursday 10-17.30 (some give you until 18.00)
Friday 10-19.00/20.00
Saturday 10-14 (some stretch it in varying degrees until 17.00)
Sundays closed

Big department stores are taking advantage of the new law, allowing for Sunday opening hours:
Mon-Sun 10-20.00

Most supermarkets:
Open all week, not all keep the same hours, but close. Mon-Sat 8-21.00 Sun 10-21 (some until 22 all week)

24-hour businesses:
7-eleven on nearly every corner in Copenhagen. Smaller selection than the supermarkets and more expensive, but better than nothing.

Closing hours like regular shops (just don't get sick).
Headache medicine and over the counter stuff can be bought at most supermarkets and newsstands.

24 hour pharmacies:
Sønderbro Apotek (located on Amager/link in Danish)
Steno Apotek (located near the Central Station/link in Danish)

Public holidays:

Current local time in Copenhagen (and other current numbers)

Trains DSB
The Copenhagen Metro (with metro map)
Journey Planner (covering all Danish trains, busses and most ferries)
Ticket and travel card information  NEW
The clip card is retired, sadly.

Local weather forecast This one is so much better/more accurate than the Danish version