What is a hurricane?

A tropical cyclone in which the maximum sustained surface wind (using the U.S. 1-minute average) is 64 knots (74 miles per hour or 119 kilometers per hour) or more.  The term hurricane is used for Northern Hemisphere tropical cyclones east of the International Dateline to the Greenwich Meridian.  The term typhoon is used for Pacific tropical cyclones north of the Equator west of the International Dateline.
Where do hurricanes hit the United States?
Names for Tropical Cyclone (Hurricanes, Typhoons, etc.)
Unfortunately, names for tropical cyclones are not standardized work\ldwide. Each region has their own naming system.
        
Atlantic
        
Eastern North Pacific
        
Central North Pacific
        
Western North Pacific
        
Western Australian Region
        
Northern Australian Region
        
Eastern Australian Region
        
Fiji Region
        
Papua New Guinea Region
        
Philippine Region
        
Southwest Indian Ocean
Isn't a Category 2 hurricane twice as destructive as a Category 1?

No, the amount of damage (at least experienced along the U.S. mainland) does not increase linearly with the wind speed.  Instead, the damage produced increases exponentially with the winds.  A 148 mph hurricane (a category 4 on the Saffir-Simpson Scale) may produce - on average - up to 250 times the damage of a minimal category 1 hurricane!

Pielke and Landsea (1998) analyzed the damage caused by various categories of U.S. landfalling tropical storms and hurricanes after normalizing by the inflation rate, increases in wealth and coastal population changes.  Tropical cyclones from 1925 through 1995 were tabulated in terms of 1995 U.S. dollars.

The following table summarizes the findings:
Intensity Cases Median Damage Potential Damage *
Tropical/Subtropical Storm 118 less than $1,000,000 ---
Hurricane Category 1 45 $33,000,000 1
Hurricane Category 2 29 $336,000,000 10
Hurricane Category 3 40 $1,412,000,000 50
Hurricane Category 4 10 $8,224,000,000 250
Hurricane Category 5 2 $5,973,000,000 500
* The "Potential Damage" values just provide a reference value if one assigns the median damage caused by a category 1 hurricane to be "1".  The rapid increase in damage as the categories go up is apparent.  (The value for Category 5 hurricanes in brackets may not be representative of true amounts because of the very small sample [two] available.)