Dictionaries and forums
This site translates between many different languages (click "translator" to choose the language you want to translate to). A part from the abundance of advertisement, it is really useful, proposes multiple translations and some examples. You can also find synonyms and definitions if you use the "dictionary" function. I have been using this site for years.
If you come over an expression or you've seen plenty of ways people write a word and you don't know which one is the right, then this is a great site to go to! I usually just write my concern right into google search engine followed by "wordreference" if needed. You can also sign in as a member and write your own question, people usually answer you quite quickly.
"Bokmålsordboka" and "nynorskordboka" are for more advanced levels. Here you find norwegian definitions for norwegian words (either in "bokmål", "nynorsk" or both). The good thing here is that you often can write in the inflected form of a verb (for instance "bought" instead of "buy" in english) and this site will find the non-inflected word for you so that you can look it up elsewhere, for instance at www.sensagent.com ;)
There are 3 tests that will give you an official certificate in Norwegian (norskprøve 2 and 3 and the advanced level test, also known as "Bergenstesten") and one that does not give any certificate (norskprøve 1). The tests certify that you have attained level A1, A2, B1 or B2/C1 (these levels are described in the CEFRL - the Common Framework of Reference for Languages).
You don't have to take them all, if you pass "Bergenstesten" for instance, you don't have to take the other tests. Bergenstesten is often demanded by some employers and universities, but not all.
As mentioned above, the "norskprøve 1" is held locally in the class (if necessary) for those who follow a community course and does not lead to any certificate.
Norskprøve 2 (level A2)
Norskprøve 3 (level B1)
Bergenstesten (level B2/C1)
Edit: The tests "norskprøve 1-3" and "Bergenstesten" are now just called "norskprøve" (Norwegian test) and you sign up for the level (A1-B2/C1) you want to test for.
Online interactive exercices
Level A1 to A2
Level A2 to B1
Level B1 to B2/C1
Håndbok i grammatikk og språkbruk (grammar and language use)
An online newspaper written in simple Norwegian (you can also subscribe to get the recieve complete paperversion and exercices that come with it).
"Utrop" is the only Norwegian news site, newspaper and television where you can find news and debates about the multicultural Norway (plus a multicultural calendar!). Some of their content is written in "lettlest norsk" (easily read Norwegian), see the link!
TV2 has created a chain on youtube for different publics (children, teenagers and foreigners). It's the normal news in a simpler and slowly spoken Norwegian.
This is for those who already know some Norwegian (I would say a minimum required is level B1, norskprøve 3), but this totally depends on you! You can also find easy reads at the library for foreigners learning Norwegian, for all levels, even beginners!