The volcanic eruption in the glacier Eyjafjallajokull in South Iceland has disrupted air traffic and resulted in many foreign travelers and Icelanders living abroad not having been able to get to their destinations in time.
Keflavik International Airport is not closed. Flights to North America are scheduled, but many flights to Europe have been delayed or cancelled.

Everybody in Iceland are alright and the travellers currently in Iceland are safe and sound.
The appropriate parties are making every effort to make their stay as pleasant and comfortable as possible.
All travellers stranded in Reykjavík due to the flight restrictions to Europe have been offered a complimentary  Reykjavík Welcome Card which gives access to all the museums and exhibitions in Reykjavík, thermal pools, public transport and more.

Here are couple of interviews with travellers in Iceland:
Travellers from Ireland that got marriaged in Iceland
Travellers from UK
Travellers from Holland
Travellers from Norway

Further information
For further information, passengers are advised to consult their airline and monitor flight schedule development. The following websites of Icelandic aviation authorities and airline operators provide valuable information on development of the situaton:
Icelandic air navigation service
Icelandic Civil Aviation Administration
Icelandair
Iceland Express