My company is not big enough to have an in-house server, so we
currently use hosting companies.  The problem is that we have not been
happy with them. The two we have used are

1)freeservers.com (communityarchitect.com)
2)ipowerweb.com

The biggest problems we encounter are these:

1)POP email v. Outlook integration is never good.  The web-based email
tends to get full and then the Outlook download on my local PC will
stop downloading.

2)The Webhosting service tends to be limited to what type of software
can run virtually.  We need one that is robust enough to be able to
run database software / C++ / and other database related programming
off of their server.

3)The email space should not run out so quickly.  Currently they
usually only give 10 MB.

4)We need to be able to offer multiple email accounts very easily,
also provide other features like sub domains.

5)The web-based email needs to have a clean, quick, easy to use interface.

6)Cost needs to be affordable ($15 - $50 a month) and reliable.

Please give me the top 3-5 web hosting companies that fit these
criteria.  The strength of their web based email is probably one of
the top concerns.  Thank you.

Look at this : http://www.50free.com/webhosting.html

  Hosting plan     FREE plan    Personal plan    Business plan    Gold plan    
  Disk space         100 MB        200 MB           1200 MB       2400 MB   
  Transfer           1,000 MB   10,000 MB         30,000 MB     40,000 MB   
  Domain name hosting   1           1                1              1   
  POP 3 email accounts  3           3              300            400   
  Email aliases         3           3              300            400   
  SubDomains            5           5              300            400   
  MySQL databases       1           1                3              5   
  12 months price     FREE       $5.95/mo        $9.95/mo      $19.95/mo   
  FTP accounts          1           1                5             10   
  Mailing Lists         0           0                1              2   
  24/7 Support         YES         YES              YES            YES   
  SMTP server            NO        YES              YES            YES    
  POP3 server           YES        YES              YES            YES   

  And also:
 
  Front Page Extensions   
  Perl support  
  PHP support    
  Instant Account Activation  
  SSI support   
  Autoresponder emails      
  Bandwidth Stats       
  Traffic Stats - WebAlizer  
  Advanced Control Panel   
  Custom ERROR 404   
  Stable Linux with Apache      
  UPS Power Backup   
  Web Based File Manager   
  Webmail