We're now into the third day of the new eruption from Grímsvötn in Iceland. So far, the ash from the eruption has fallen only on Iceland and the North Atlantic Ocean as the plume remains ~6-9 km / ~20,000-30,000 feet tall (down from close to 15-20 km / 50-60,000 feet over the weekend). significantly so on parts of Iceland (Icelandic), reaching as far Reykjavík (albeit in µg/m3 concentrations) and causing the closure of the largest airport on the island, but flights should resume today. However, it is beginning to look like some flights in the United Kingdom and Ireland might begin to be disrupted by the ash as early as tomorrow if the volcano continues to erupt and the VAAC models are accurate. The latest ash model from the London VAAC (see below) shows the ash drifting over Greenland and also sweeping back down to the south towards northern Europe. Even so, the likelihood of a widespread airspace closure over all of Europe is much lower than in last year's Eyjafjallajökull eruption, for both volcanological and political reasons (I suspect).
UPDATE 12:30 PM (Eastern): It looks like at least 36 flights were cancelled in Scotland by Loganair due to the encroaching ash. However, the UK government says it is "better prepared" for this ash than last year. Some airspace over Greenland is also closed as well.
UPDATE 2:15 PM (Eastern): This is a pretty amazing animated GIF of the opening stages of the eruption. Textbook plume development and spreading. {Thanks to Luis for posting it in the comments}. To go with that, check out the satellite images of the ash plume punching through the clouds.