We present the first large statistical study of extreme geomagnetic storms based on historical data from the time period 1868 – 2010. This article is the first of two companion papers. Here we describe how the storms were selected and focus on their near-Earth characteristics. The second article presents our investigation of the corresponding solar events and their characteristics. The storms were selected based on their intensity in the aa index, which constitutes the longest existing continuous series of geomagnetic activity. They are analyzed statistically in the context of more well-known geomagnetic indices, such as the Kp and Dcx/Dst index. This reveals that neither Kp nor Dcx/Dst provide a comprehensive geomagnetic measure of the extreme storms. We rank the storms by including long series of single magnetic observatory data. The top storms on the rank list are the New York Railroad storm occurring in May 1921 and the Quebec storm from March 1989. We identify key characteristics of the storms by combining several different available data sources, lists of storm sudden commencements (SSCs) signifying occurrence of interplanetary shocks, solar wind in-situ measurements, neutron monitor data, and associated identifications of Forbush decreases as well as satellite measurements of energetic proton fluxes in the near-Earth space environment. From this we find, among other results, that the extreme storms are very strongly correlated with the occurrence of interplanetary shocks (91 – 100 %), Forbush decreases (100 %), and energetic solar proton events (70 %). A quantitative comparison of these associations relative to less intense storms is also presented. Most notably, we find that most often the extreme storms are characterized by a complexity that is associated with multiple, often interacting, solar wind disturbances and that they frequently occur when the geomagnetic activity is already elevated. We also investigate the semiannual variation in storm occurrence and confirm previous findings that geomagnetic storms tend to occur less frequently near solstices and that this tendency increases with storm intensity. However, we find that the semiannual variation depends on both the solar wind source and the storm level. Storms associated with weak SSC do not show any semiannual variation, in contrast to weak storms without SSC.