This is a difficult question because there are several volcanoes that are well known but I would say that Mt Eyjafjallajökull (Eyjafjallajokull in English spelling) is the most famous volcano nowadays. I will use the English spelling below since the Icelandic letters get scrambled in some browsers.
Mt Eyjafjallajokull became famous in 2010 when it erupted stopping all the air traffic between North-America and Europe. The eruption took place in two episodes, the first episode started in March 2010, the second episode started in April 2010. It’s the second episode that took place beneath the glacier on top of the volcano resulting in an ash cloud that the winds blew to Europe. That’s why the volcano made the international headlines for five days or so.
Is it possible to see Mt Eyjafjallajokull? Yes, it is. We are passing the volcano when we drive to the south coast seeing and visiting all those beautiful places along the south coast. If clouds permit we can see and take photos of the volcano.