I'm trying to do something like this but for quoted emails, so this
On 2014-07-11 at 03:36 PM, <[email protected]> wrote:                                                                                                                                                                                                                                                       
>Hi Everyone,                                                                                                                                                                                                                                                                                                                 
>                                                                                                                                                                                                                                                                                                                             
>                                                                                                                                                                                                                                                                                                                              
>                                                    
>I love spaces.
>                                                                                                                                                                                                                                                                                                                             
>                                                                                                                                                                                                                                                                                                                          
>                                                                                                                                                                                                                                                                                                                          
>That's all.                                                                                                                                                                                                                                                                                                                       
Would become this
On 2014-07-11 at 03:36 PM, <[email protected]> wrote:                                                                                                                                                                                                                                                       
>Hi Everyone,                                                                                                                                                                                                                                                                                                                 
>                                                                                                                                                                                                                                                                                                                             
>I love spaces.
>                                                                                                                                                                                                                                                                     
>That's all.   
Thanks
Another awk-based solution:
awk '{ /^>\s*$/?b++:b=0; if (b<=1) print }' file
Breakdown:
/^>\s*$/?b++:b=0
    - ? :       the ternary operator
    - /^>\s*$/  matches a blank line starts with ">"
    - b         variable that counts consecutive blank lines (b++).
                however, if the current line is non-blank, b is reset to 0.
if (b<=1) print
    print if the current line is non-blank (b==0)
          or if there is only one blank line (b==1).
Assuming that each visual line is a proper logical line (string of characters ended with a \n), you can dispense with the rest of the tools and simply run uniq(1) on the input. 
Example follows.
% cat tst
>Hi Everyone,
>
>
>
>I love spaces.
>
>
>
>That's all.
% uniq tst
>Hi Everyone,
>
>I love spaces.
>
>That's all.
%
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