Usually I develope my projects locally on my pc. Needless to say that you sometimes have to send an email from your script to external mail to check if everything is fine. So you need to configure your system in a way that your local apache webserver is able to send mail to external addresses.
I always use XAMPP for Windows because it contains everything you need for developing PHP applications as well as all the stuff for sending mails: fake sendmail und Mercury Mail Transport System. I reference to XAMPP 1.6.5 (for Windows) and Mercury 4.5 here. Mercury is already pre-configured in XAMPP - all settings that I don't explicitly address stay as they are

I'm writing this because I'm not a mail professional and read a lot of tutorials and none of them really worked. So I extracted what I needed and put it all together. An important assumption for this tutorial is that you have your own SMTP server, for example the one that your webspace hoster provides.

So let's get started:

1. start Mercury (using the XAMPP Controlpanel) and then open the admin panel.
2. first of all we disable the HTTP server of Mercury so that it doesn't conflict with the apache:
   1. "Configuration" -> "Protocol modules"
   2. disable the check "MercuryB HTTP web server"
   3. I also disabled "Mercury IMAP4rev1 server" because I won't need that one
   4. leave the window opened, we'll need it immediatly
3. to be able to send external mail we have to disable "MercuryE SMTP end-to-end delivery client" in the same dialog and enable "MercuryC SMTP relaying client". Click "OK" and restart Mercury!
4. now let's configure Mercury in general:
   1. "Configuration" -> "Mercury core module", tab "General"
   2. we want to send from localhost, therefore we check if "localhost" is the value of "internet name for this system" and adjust that if not
   3. all other settings stay the same as they are already configured, but we'll have a look to the checkboxes beneath:
   4. disable all but "Send copies of all errors to postmaster"
   5. check under the tab "Local domains" if the entry "localhost (local host or server) localhost (internet name)" is there, if not, add it
   6. click "OK" and leave the dialog
5. next we focus on the MercuryS SMTP Server for outgoing emails:
   1. "Configuration" -> "MercuryS SMTP Server"
   2. choose the tab "General" and add a wonderful name for your SMTP server under "Announce myself as", simply fill in any name, I've chosen "CS SMTP".
   3. under "Listen on TCP/IP port" fill in "25", that's the SMTP port
   4. add "127.0.0.1" to "IP interface to use", that's the local IP of your pc. With the IP of the pc within the network (192.168.0.X) it doesn't work (at least for me)
   5. now we limit the access to the server so that only our local machine can access it:
      1. under "Connection Control" click on "Add restriction" and add the IP range from "127.0.0.1" till "127.0.0.1" (it's that simple, isn't it?)...
      2. and select "Allow connections"...
      3. and leave all checkboxes deselected
   6. with a click on "OK" we quit the dialog and we're looking forward to the next one
6. now let's configure the MercuryP POP3 Server:
   1. "Configuration"-> "MercuryP POP3 Server", select the tab "General"
   2. "Listen on TCP port" -> "110" and "IP interface to use" -> "127.0.0.1"
   3. choose the tab "Connection control" and proceed as already written under 5.5 (see above)
   4. that's it already, leave the dialog by clicking "OK"
7. now we have the important one "MercuryC SMTP Client"
   1. "Configuration" -> "MercuryC SMTP Client"
   2. to send mail to external addresses we need to have an external SMTP server. If you're renting webspace somewhere and have mail included then you normally have access to a SMTP server. My webspace is hosted at HostEurope and I'll use the SMTP of my domain. Without such an external server the whole thing won't work because domain names won't be resolved among other things. I've chosen this path because I didn't feel like configuring around the whole day.
   3. enter the address of your SMTP under "Smart host name", for example "mail.meinedomain.com"
   4. depending on the way you access the server fill the values under "Connection port/type":
      1. for a "normal" SMTP that would probably be port 25 and "Normal (no SSL encryption)"
      2. I access my SMTP via SSL, that would be port 465 and "SSL encryption using direct connection"
      3. if you have other parameters simply try around a little
   5. we finally fill in the "Login username" and the "Password" that normally is supplied by your webhost and we've nearly finished...
8. let's check the Mercury users that are normally pre-configured:
   1. "Configuration"-> "Manage local users"
   2. there should be at least the users "Admin" and "postmaster", both with administrative rights. If not you have to add them.
9. now we finished with Mercury, but we still need to configure PHP for sending mail with our scripts:
   1. we search and open the appropriate php.ini, using XAMPP you find it under "xampp/php/php.ini" in newer version and under "xampp/apache/bin/php.ini" in older versions
   2. we search for "[mail function]"...
   3. and we add/adjust the following:
      1. "SMTP = localhost"
      2. "smtp_port = 25"
      3. "sendmail_from = postmaster@localhost"
   4. save the php.ini and restart the Apache
10. now everything should work! But we'll test it first:
    1. within Mercury choose "File" -> "Send mail message" and send an email for testing purposes, I've chosen to send it to my googlemail account
    2. if the windows in Mercury are at sixes and sevens, choose "Window" -> "Tile" enjoy the view
    3. within the window "Mercury Core Prozess" we'll see our test mail at first:
       1. "13:38:41 JOB XXXXXX: from postmaster@localhost (local) To: XXX@googlemail.com (non-local) (JOB XXXXXX) -OK"
    4. the mail was received in Mercury and processed, after some seconds the window "Mercury SMTP client (relay version)" should show some actions:
       1. "05 Jan 2008 13:39, Servicing job XXXXXX ...OK"
       2. if you see this message, everything went fine and the mail was sent!
       3. if you don't get the message you have to find out why, possible reasons could be:
          1. wrong connection values for the SMTP server
          2. SMTP server doesn't allow relaying (from your host)
    5. now we'll test the whole thing from a PHP script and we'll write a wonderful one-liner into a PHP file:
       1. "mail('xxx@googlemail.com', 'Mercury test mail', 'If you can read this, everything was fine!');"
       2. call the PHP file within your browser, a command window should pop up shortly (or maybe not), it's from the fake sendmail of XAMPP, and focus back on Mercury:
          1. the produre is the same as above only that the SMTP server receives the mail from php before everything else happens
          2. you can watch this in the window "Mercury SMTP Server" and should see something like this: Mercury SMTP

I hope that worked for you, if not, feel free to leave a comment but as I already said, I'm not a professional but I'll help you as far as I can!

EDIT:
If you get the error message "SMTP server response: 553 We do not relay non-local mail, sorry." while sending from PHP go to Mercury under MercuryS -> Connection Control -> "Uncheck Do not Permit SMTP relaying to non-local mail" an check this option. Should fix the problem. Thanks to ron!

These are other links and tutorials that is used for research. These might help when setting up Mecury Mail

• How To: Setup Mercury Mail on an XAMPP Package - This video is in my video library
• Setting up Mercury SMTP for XAMPP
• Configure XAMPP Mercury Mail
• Configure Mercury mail transport system for external mail sending
• Configure Mercury mail transport system for external mail
• Using Mercury mail to send mails - forum thread
• Mercury mail - forum thread