I lived in Reykjavik at the time of the 2010 eruption of Eyjafjallajökull, and I had a friend with a giant jeep... So we drove to about 500m from the hole in the ground spouting lava (safe, open to the public, quite a few people there) and had the nature experience of a lifetime.
We literally called it the tourist volcano, because you could get so close and still be safe.
The problem with ash is due to how jet engines work: they push air through them, which is heated up significantly. The ash melts and becomes glass which can damage the engine.
> Isn't it dangerous to fly over erupting volcanos?
I'm not a pilot, but I trusted the judgement of the pilot and felt like it was worth the risk. The pilot planned our approaches carefully and though we got quite low, we were always circling around rather than going directly over the fissure. At the time the Icelandic aviation authorities had issued a warning (but no closure) for the airspace around the volcano.
The spectacle was so moving that fear wasn't a prominent emotion. The only hair-raising part was when we flew too low over some lava (shortly after this photograph was taken: https://www.flickr.com/photos/41812768@N07/15145875322/in/al...). The turbulent air from the heat shook the aircraft so violently that my headset came off.
When there are ongoing eruptions in Iceland, there are usually several companies that offer flights or helicopter tours to go see them. The tours normally cost $1-2k per person. Another option is to go hang out at the domestic airport in Reykjavík. Talk to a few people and you may find a private pilot who just wants to split the fuel cost.
Photos: https://www.flickr.com/photos/41812768@N07/albums/7215764724...
If you're planning a visit to Iceland I'm happy to answer questions here or by email.