Tested in Windows 7 x64:
This is a two step process.  The user's default browser is in key:
HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\FileExts\.html\UserChoice\Progid
Common browser Key Name:
- IE: IE.AssocFile.HTM
 
- FireFox: FirefoxHTML
 
- Chrome: ChromeHTML
 
- Opera: Opera.HTML
 
Replace <KEY NAME> below with one of the values above to find the executable:
HKCR\<KEY NAME>\shell\open\command
Autohotkey script to display the default browser path and executable:
MsgBox % "Default browser: " Browser()
Browser()
{
    ; Find the Registry key name for the default browser
    RegRead, BrowserKeyName, HKEY_CURRENT_USER, Software\Microsoft\Windows\CurrentVersion\Explorer\FileExts\.html\UserChoice, Progid
    ; Find the executable command associated with the above Registry key
    RegRead, BrowserFullCommand, HKEY_CLASSES_ROOT, %BrowserKeyName%\shell\open\command
    ; The above RegRead will return the path and executable name of the brower contained within qoutes and optional parameters
    ; We only want the text contained inside the first set of quotes which is the path and executable
    ; Find the ending quote position (we know the beginning quote is in position 0 so start searching at position 1)
    StringGetPos, pos, BrowserFullCommand, ",,1
    ; Decrement by one for the StringMid to work correctly
    pos := --pos
    ; Extract and return the path and executable of the browser
    StringMid, BrowserPathandEXE, BrowserFullCommand, 2, %pos%
    Return BrowserPathandEXE
}