Even if Geysir, the most famous of Iceland's geysers, is the namesake for all the world's geysers and the group of periodically spouting hot springs as such, Icelanders are regarding "Geysir" as a proper name and are using the term "Goshver" (gushing hot spring) for the class of erupting hot springs. This may cause some confusion if someone is browsing through the Icelandic literature in search for reports about geysers.
In general, the activity of Iceland's geysers is subjected to energy surges by earthquakes to a much higher degree compared to some other geyser fields on earth, for example Yellowstone. So their pacemaker is the activation by an earthquake and decline thereafter at individual rates.
Of course, Iceland is one of the most important geyser sites worldwide. But the question arises, how many and which geysers are to be found. Books and other publications often state a number of 30 geysers without giving a detailed list. Well, let's see about it. Unfortunately, information about small and often short living geysers is quite hard to come by, if existing at all. Without systematic observation the problem is on one hand to distinguish between perpetual spouting or true geyser activity, on the other hand that remote features may erupt unnoticed. Therefore, the list focuses on the mostly well known and scientificly documented named geysers. Unnamed geysers, usually inconspicuous small, or remote, or short living, or very recently observed for the first time, are only included if they have shown an noteworthy eruption height of 1 m / 3 feet or more:
Geysir (active, but currently in phase of minor eruptions, location Haukadalur)
Árhver (active, location Reykholt in Borgarfjörður, Western Iceland)
Reykholtshver (active, but covered by cistern roof, location Reykholt in Árnessýsla, Southern Iceland)
Stórihver (status unknown, location Austur-Reykjadalir in Fjallabak Nature Reserve)
Kátur (status unknown, location Austur-Reykjadalir in Fjallabak Nature Reserve)
Above I have listed some geysers as "dormant", which are regarded as extinct by other authors. The criterion for me to keep them on the list is that they are still fed subterranean with hot water and there is no indication that their plumbing system may be clogged or otherwise damaged. And even if for a long time some of them have been quiet, some have been acting as perpetual spouters, and others have been reaching as boiling or bubble-shower springs only insignificant eruption heights, history has taught us that on the next earthquake they may be back as true geysers.