There are over 200 named waterfalls in Iceland, so you'll definitely want to visit one (or several) while you're there. How you choose which ones to visit depends on where your home base is and how long you are staying. Iceland can be a common stop-over for North Americans on the way to or from the rest of Europe. On stop-overs, visitors commonly take in the Golden Circle, which consists of Þingvellir National Park, Geysir Geothermal Area. and Gullfoss waterfall.
If you're staying in Reykjavik, there's some others nearby as well - Brúaráfoss, Glymur (one of the highest), Hraunfossar, Barnafoss, Seljalandsfoss (one you can walk behind), and Gljúfrabúi. Some are easier to get to than others, so you'll definitely want to be prepared before visiting. If time and transportation aren't an option, there are some must-see waterfalls in other parts of the country as well. The Svartifoss (in Skaftafell) is named after the dark lava columns that surround it - these are said to be the inspiration for Hallgrimskirkja in Reykjavik. Goðafoss, waterfall of the gods, is one of the largest waterfalls in the country. Háifoss in South Iceland is one of the tallest in Europe and has another waterfall Granni just next to it. Dettifoss in North Iceland is the most powerful waterfall in Europe - so much so that you can feel the earth tremble beneath your feet when you stand close to it. Dynjandi waterfall is worth a visit as well - it's twice as wide at the bottom as it is at the top and consists of a row of several falls.