Summer in Iceland is very pleasant and the sun barely sets, a natural phenomenon called the Midnight Sun. You'll have the least chance for rain during June and the weather in Iceland stays mild until late August. Come mid-September, though, almost all of the summer activities will be closed until May of the following year.
The colder part of the year is also the time when flight prices to Iceland fall drastically and suddenly the local hotels cut their prices in more than half. Budget travelers wondering when to go to Iceland should aim for February or March. They have more daylight than the earlier winter months.
If you decide to go to Iceland in the winter, get ready for very cold temperatures and only 3-4 hours of daylight (called the Polar Nights). If you can endure that, the question of when to go to Iceland suddenly becomes much harder. Because Iceland also has much bolder things to offer in winter: Never-ending nightlife in Reykjavik, the viewing of the beautiful Northern Lights, and plenty of outdoor activities in the snow!
Now that you know what to expect, it should make it a little easier for you to decide when to go to Iceland.