So, for starters, here are some awesome apps which will help you out and about in Copenhagen (and the rest of Denmark).
Fetch your phone or save the webpages as favorites as they will help you. Plus they are free! :)
Byenspuls - "Pulse of the City". An app that shows how the S-trains run. All delays on every train is shown and updated live. Available for both Android and iPhone. Also available as website: http://byenspuls.dsb.dk/byens_puls/ByensPuls.html
Rejseplanen - "Itinerary". An app that makes it super easy for you to plan your trip from anywhere to whereever you like. Available in English and German as well. Tracks times for both buses, S-trains, InterCity trains, LynTrains and Øresundstrains and Metro. Also comes as website: http://www.rejseplanen.dk/
1415 App. This app is instead of the ticket machines in buses, metro and trains. You can buy tickets with it for travel with public transportation. Available for iPhone (not sure about Android yet, but maybe it's up and running by the time you read this). 1415 is also the phone number you use, if you buy your ticket as SMS ticket.
Hvad har åbent nu - "What's open now?". This app shows open stores nearby (works for about 3000 stores). Really usefull for when you are not on Campus, where DøgnNetto will save you since it's almost always open. Available for both Android and iPhone.
AOK Guide - "Everything About Copenhagen Guide". Not sure if this app is avaliable in English, but it's graphic and simple to understand, so I don't think it will be a big problem if it doesn't. Shows all bars/clubs/restaurents/theatres/scenes/whatever where you are. Available for both iPhone and Android. Also a website: http://www.aok.dk/ (which is in English also)
Visit Copenhagen - The Official City Guide. This app is in English and shows everything you need to know before and during your stay in Copenhagen. Available for both iPhone and Android.
The list will be updated during the semester, so watch out - and feel free to recommend any apps or websites that can make life in Copenhagen and Lyngby more awesome for you all. :)