opening ports to the internet
I do. I use Mocha VNC Lite on my iPad and iPhone. Simple, free, but gets the job done. Make sure you have port 5900 mapped if you use a router.
I realise this is a VERY old thread but....
Do
NOT open port 5900 on your router to your pc/mac/whatever running a VNC server; VNC has pretty much zero security and doing so
will result in some spotty hacker somewhere remote controlling your computer.
If you want to use VNC remotely, set up an ssh server on the same machine as the VNC server (preferably don't use the default ssh port 22) and open that port through your router. (there's a mac orientated description of this
here).
As an added bit of security, use public/private key encryption (RSA for preference) and disable password logons.
I don't have an ipad/iphone but the software to do all this free is available for android (and works because I have set it up and use it) so I'd guess the same is true for ios
Note that the above shenanigans requires you to do some typing at a terminal and have some understanding of what you're doing. If you aren't comfortable with that then you're out of luck with free and you're looking at paying for some software

.
When I get back to my mac I'll be trying out the vnc:// route in safari. I've tried chicken of the VNC and whilst it works it crashes a bit, doesn't scale well on my air (pc I'm viewing has a higher vertical resolution so the bottom of the screen gets chopped) and does funky stuff when in fullscreen. And it doesn't seem to support jpeg compression so its a bit sllloooww.