The first type of geyser we will talk about is called a fountain or pool geyser. Fountain geysers are characterized by a pool of hot water. When the geyser is not active, it looks just like a very deep pool of steaming water; however, this is actually the place where the water spews out. If you were to view the top of the geyser when it was about to erupt (this is not recommended), you would see the pool of water drop down into the geyser right before it erupts. Some examples of fountain geysers are: The Great Geyser in Iceland, Narcissusin in Yellowstone Park, and Kotegu in Russia (Geysers).
        The next type of geyser is called a cone geyser. Cone geysers are also known as column geysers and were named for the cone that usually forms around the geyser's mouth. This cone is created over hundreds, or even thousands, of years from minerals coming out of the geyser when it erupts and building up around it. If you look on the right hand side of this page, you can see a picture of a famous cone geyser "Old Faithful".
        Another interesting type of geyser is known as a cold-water geyser. This type of geyser has a completely different method of operation as the other types of geysers discussed so far. Cold-water geysers are driven by CO2 dissolved in water building up inside the geyser shaft (Glennon, 2005). Once enough gas is in the geyser the air pressure will overcome the hydrostatic pressure of the water causing it to erupt like a heat driven geyser would.
        The last type of geysers (more of a subtype) we will discuss are called perpetual spouters. These are geysers that erupt all the time. Since they are constantly erupting they do not shoot water and steam as high into the air as a normally geyser would. Nevertheless, perpetual spouters do have "phases" when they are erupting higher into the air, and times when the eruptions are not as high. It is also possible for a geyser to operate as a normal geyser for periods of time, and as a perpetual spouter other times.

Old Faithful is one example of a cone geyser
Source: http://www.swerdloff.us/Yellowstone/OldFaithful.html