Throughout the world, there are various famous lists of "peaks", such as the Eight Thousanders in the Himalayas, the "Fourteen Thousanders" in Colorado, the "Eleven Thousanders" in the Canadian Rockies, and the Munro's of Scotland (peaks over 3000 feet). The general idea of these lists is simply to list how many "peaks" there are in a given area that exceed a given height. These are "height based" lists.
A list is two things: a certain "class" and a certain "area". Eg: All 11,000ers in the Canadian Rockies.
Any list eventually runs into the need to have a rule as to what constitutes a separate peak, otherwise the list just keeps growing as subpeaks are promoted to full blown peaks. Eg: In the Rockies, first there was North Twin and South Twin. But now the list commonly referred to in various publications also has a "Center" Twin, and a West Twin, making up 4 twins. The most common definition of "separateness" is to have a rule that any peak on the list must have a vertical separation of a certain amount. For example, the Colorado rule for separate peak is a 500 foot vertical separation. The name these days for this vertical separation is "prominence". Nowdays, most peaklists are moving toward having some measure of prominence in their definitions.
Originally, all the famous lists were based mostly on height, with prominence only used as a means of determining what is allowed as a "separate peak". However, once prominence became formalized, new lists emerged which were based ONLY on prominence. The most famous of these "prominence only" lists is a list called the "ultras". An ultra is a peak with 5000 feet of prominence. The original definition was 5000 feet, but then was changed to 1500m (4921') to make it international. Peaklist.org says there were 1,524 peaks with 1500m prominence as of June 10, 2007. As of 2012.08.22, wikipedia only lists 1515 ultra prominent peaks with 5000 feet. (which makes sense, because 5000' is slightly higher than 1500m). See Ultra Prominent Peaks in Wikipedia. It is possible that these lists could change a bit due to newer surveys, but it is more stable than any "height only" list, because it doesn't depend on anyone's opinion as to what is a separate peak and what isn't.
In addition to height based lists, and prominence based lists, there are hybrid lists, which combine both height and prominence. For example, an interesting list is the list of all peaks in Canada over 3000m, and with a prominence of 1000m. Such lists are sometimes more interesting than pure prominence lists, because the height threshold ensures that the peak is truly of mountaineering significance. The height rule eliminates the possibility of a 1500m forested bump on an island. Such a list could be called a list of 3000/1000ers.
One other factor that is sometimes considered when making up lists is how far the peak is from some other peak. Eg: A peak that is less than 1 km away from another peak on the list is not considered a separate peak, regardless of prominence. This property is called "Isolation". Although there is some recognition of the notion of isolation in certain famous lists, it is not usually included in the definition.
In Bivouac, we have three important "classes" of peaks:
Rather than giving each class a name such as "ultra", we refer to them as "P2000's, P1000's and P500's peaks. There are 81 P2000's in North America. How many have you climbed?
Type Prominence --------------------------------
P2000 2000m of prominence
P1000 1000m of prominence
P500 500m of prominence