In an here document you don't need to escape quotes.
Inside your here document you missed the closing tag for the table.
If you want to print a string that contains double quotes you might use single quotes for that string eg:
print '<tr><td><a href="'.$rank{$_}{url}.'"><center><b>';
please correct your line as you omitted the ' for the hits:
for (sort {$rank{$b}{'hits'} <=> $rank{$a}{'hits'}} keys %rank)

Have a nice day
All decision is left to your taste
Update
as far as I came with it. Better try to use cgi.pm. It is easy and helps you a lot.

#!/usr/bin/perl -w

use strict;


my $memberListFile = "members.txt";
my $hits;
my %rank;
my $user;
my $email;
my $username;
my $sitename;
my $url;
my $button;
my $desc;

print "Content-type:text/html\n\n";

open(USERS, $memberListFile) die ("can't open $memberListFile: $!");

while(<USERS>)
{
    chomp; # ah, cleverly working on $_
    ($user,$email) = split(/\|/);
    my $USR; # better find some naming conventions, for me looks this 
+like a CONSTANT in the source
        
    $user .= ".txt"; # still ugly, but better compose filenames before
+ using them (makes debugging easier)
    open (USR,"$user") or  die ("can't open $user: $!");
    $USR = <USR>; # scalar context ? why? do all these files only have
+ one line?
    close(USR);
   
    ($username, $sitename, $url, $email, $button, $desc, $hits) = spli
+t(/\|/, $USR);
   
    $rank{$username} =
    {
        'url' => $url,
        'email' => $email,
        'button' => $button,
        'desc' => $desc,
        'hits' => $hits,
        'sitename' => $sitename,
        'user' => $username
    };
}

print <<eof;
<font face="verdana" color="black">
<table WIDTH="75%" border="1" bordercolor="black" cellSpacing="0" cell
+Padding="0" align="center">
    <tr bgcolor="#000080">
        <th>
            <font face="verdana" color="white">
                Site
            </font>
        </th>
        <th>
            <font face="verdana" color="white">
                button
            </font>
        </th>
        <th>
            <font face="verdana" color="white">
                Hits
            </font>
        </th>
    </tr>
eof

foreach (sort {$rank{$b}{'hits'} <=> $rank{$a}{'hits'}} keys %rank) 
{
    # oh ouh here it is not clever to work with $_
    print <<eof;
    <tr>
        <td align="center">
            <b>
            <a href="$rank{$_}{url}">
                $rank{$_}{sitename}
            </a>
            <br />
            <font face="verdana" size="1">
                $rank{$_}{desc}
            </font>
            </b>
        </td>
        <td align="center" width="88">
            <img src="$rank{$_}{button}" height="31" width="88">
        </td>
        <td align="center">
            $rank{$_}{hits}
        </td>
    </tr>
eof
}

print "</table>\n</font>";
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