I second this advice, having done it. I flew one-way from Seattle to Dublin in 2010 with no plan beyond the first week. 25ish cities and 4.5 months later, I flew back. You ll figure it out as you go.
But, a warning from experience: when you fly one-way to another country where you ll go through immigration, always pre-book travel OUT of that country as well, and have printed (on paper!) proof to show border control. Fortunately this doesn t apply between most European countries due to the Shengen area. Immigration is not the part of the trip where you want to wing it. Always make sure you understand the visa and border crossing rules in advance.