This is howto control your home pc from anywhere using your Android device.
iPhone users should be able to use this howto aswell but use a VNC client for iPhone.

All software and services described below are free for personal use.

1) Download and install tightvnc on your home PC. Leave everything default,
don't forget to add two different passwords at the end of the installation.
http://www.tightvnc.com/

2)On your router settings enable ports 5800 and 5900 forwarding to your home PC
Read more:
http://www.tightvnc.com/faq.php#portfwd

3)If you have a dynamic ip or if you dont know what type you have:
Sign up with wwwdnsdynamic.org - free DDNS service(Dynamic Domain Name System)
You can use their web client or install their windows client, add it to your autorun folder
and forget about it.
After that you should be able to connect to your home PC from anythere by
typing in the browser: yourname.dnsd.info - or whatever you chose at wwwdnsdynamic.org

3)On your Android device - download and install androdiVNC application from Play Store.

NB! If during installation of any of the above your windows firewall will pop up
- select allow, otherwise it will not work.

Optional: for added security you can install VPN (virtual private network)
on your router if it allows that. On your Android device you will connect to your home network by going
to Settings -> Wireless and Network ->VPN settings