Is Norway significantly more expensive than other European destinations?

victoriah wrote in her answer:

It's a generally accepted fact that the Scandinavian countries are the most expensive places to travel. But personally, having travelled a lot within Europe and within Scandinavia, I don't think it's SO much more expensive in comparison to the rest of Europe.

I'm from Finland—another Nordic country generally considered expensive—and my understanding (anecdotal, from friends and colleagues who have visited or lived in Norway) is that Norway is significantly more expensive than Finland.

So the short answer is: Yes, Norway most certainly is significantly more expensive than European destinations in general. It resembles Switzerland in this regard.
^{Which is not to say that you shouldn't visit! :-)}

On the other hand, if you have the possibility to work there, it's a great place to earn money. :-)

Some examples: A beer in a bar in Oslo can set you back as much as 10 € (~80kr). In Helsinki 4-6 € is normal and considered expensive by most foreigners. Price for a dorm bed in an Oslo hostel seems to range from 29 to 51 € (!), while in countries like Germany or France I've generally paid around 15-25 €.

In any case, I guess victoriah is right in that if you're careful you can keep your costs relatively low even in Norway. One obvious way to save heaps would be to pay nothing for accommodation, through CouchSurfing or a similar service, if that's your cup of tea. Norway has a high density of hospitable people opening their homes to strangers. One British CS guest of mine, for example, had great experiences in Norway and said it was much easier to find a host there compared e.g. to Baltics.

Edit: I just noticed that the Norway guide on Wikitravel has a good section on costs. Quoting a little bit:

Norway is an expensive country. While it is possible to travel in Norway on a limited budget, some care must be taken. Because labour is costly, anything that can be seen as a "service" will in general be more expensive than you expect. Travel costs can also be a killer, because the country is large and distances long, so a rail or air pass can save you a lot of money.

As rules of thumb, subsisting on under 500 kr/day (~65 €) will be difficult even if you stay in hostels and self-cater, with 1000 kr/day allowing a more comfortable mid-range lifestyle and over 2000 kr/day needed for good hotels and restaurants.

Update: Here are some actual statistics

(Which happen to support my anecdotal knowledge perfectly.)

A recent (2012) Eurostat study on prices of goods and services found that if EU zone average price level is described with 100, the most expensive countries in Europe are:

1. Switzerland 162 (i.e., prices are 162% of the EU27 average)
2. Norway 151
3. Denmark 142 (the most expensive EU country)
4. Sweden 128
5. Finland 125 (the most expensive eurozone country)
6. Luxembourg 122
7. Ireland 117

Looking at prices of alcoholic beverages & tobacco only, Norway is far and away above everyone else at 250 (followed by Iceland 155, UK 147, Sweden 145). Also for food & non-alcoholic beverages Norway is the most expensive: Norway 164, Switzerland 156, Denmark 136, Sweden 120. The same goes for restaurants & hotels: Norway 184, Swizerland 157, Denmark 154, Sweden 147. In other words, in things most relevant to a traveller, Norway is the most expensive country in Europe.

The cheapest European countries included in this study were Macedonia (45), Albania (51), Bulgaria (51), Serbia (57), and Bosnia and Herzegovina (57), with Bulgaria (51) and Romania (60) being the cheapest EU countries.

Sources:

• Eurostat: Price levels varied in 2011 from 51% of the EU27 average in Bulgaria to 142% in Denmark (PDF)
• HS: Eurostat: Suomi kallein euromaa

With Norway, it is easier to point out what is cheap rather than what is expensive.

In contrast to iHaveacomputer's answer, I find all kinds of fruit and vegetables cheap. That is because the fruit and vegetables are subsidized, and would otherwise cost a fortune.

First Price is a low cost brand that provides cheaper alternatives, sometimes equal in quality to its competitors. First Price products can be found at Kiwi or Meny (both grocery stores) and probably some other stores.

Landlord is a brand similar to First Price, but I only remember seeing their products at Rema 1000 (another grocery store).

I've never been to Norway, but I lived with a norweigan guy in Ireland for a year. Ireland is/was more expensive that most the rest of europe. He said that coming from Norway was great cause Ireland was cheaper than home, an experience not many visitors can say!

I've heard anecdotially that Norway is more expensive that the rest of europe.

For you as a Backpacker, Norway will be on pretty much the same level as for example Germany, France or Sweden, but slightly more expensive than eastern Europe. The Hostel rates should be about the same.

However some things are more expensive in Norway: Beer and Alcohol - i went out on a saturday with something equal to 20 Euro, and i got 2cl of whisky and some change for it... Tropical fruits like Bananas, Oranges and everything that wont grow in cold climate costs more, especially in all the small villages up north.

Domestic flights are also way more expensive (possibly because there is not much demand for it because few people live up there; and they only use small planes), and im not aware of any budget airline. Take the train or bus instead, unless you are in a hurry.