I can add some comments to Tyler Durden's answer. Viking ships were not optimized for the open sea sailing performance. But they were good for rowing, travel near the shore and in the rivers. They were relatively long and narrow and had a shallow draft. As a result they could not carry much sail. The rudder was not invented yet, they used a steering paddle. The single small square sail they had is a poor performer except downwind. As I already said in my comments, rowing in the open ocean is not an effective way of transportation, especially in the presence of waves, wind and current. Of course, some ocean travels in these ships are known and well recorded. They certainly colonized Greenland and probably had a colony in North America. But I suppose these trips depended on favorable winds and a lot of luck.
Sailing boats, which are optimized for sailing have very different hull shape and different sails and rigging.
On the other hand, travel range near the shore (the thing they mostly did) was unlimited, assuming you can refill water and food on shore. And we know from history that they traveled thousands miles along the shore.
One also has to take into account that open sea travel in antiquity and Middle age was only possible in summer in most cases.
EDIT. Here is a book that analyses performance of modern replicas of ancient and medieval ships: Sailing into the Past: Learning from Replica Ships
By Jenny Bennett (2009). It is not freely available but can be searched on Google books. It mentions a sea trial of a replica of a longship. The speed achieved windward was about 1 knot, downwind from 4 to 8, rowing about 3 knots.
Of course, the speeds achieved in a trial are not the average speeds over long trips.
ADDED on Aug 12, 2015. Yesterday, I saw an excellent movie:
which documents a trip from Denmark to Ireland on a replica of a large Viking longship. The movie very well confirms what I wrote. 1. Rowing in the ocean waves is not an option. 2. Sailing against the wind was impossible or useless. 3. Even in the best season, you cannot be sure how long will the travel be.
Few modern people would survive such a trip under true "Viking-time conditions", I mean without modern high-tech cloths and radio weather forecast.
Perhaps the correct question would be not "how long does it take", but "what was the survival rate in these travels". Were the loss of life in sea larger or smaller than in combat ?