How well does Apple Remote Desktop work over the Internet? I have a few family members with Macs that I'd like to be able to help if they have questions or get stuck, and I've been looking into various solutions to be able to remotely connect to their computers over the internet. In the past I've mainly used iChat, but it sometimes just doesn't work (and I do have a few members in my family that have a bit of trouble accepting the screen sharing invitation). My typical fallback is Skype which nearly always works, but I don't have any control over the screen so I have to walk them through what they need to do.

Now that Apple Remote Desktop is available in the Mac App Store for $80, I'm wondering if it does what I need. Namely, I'd like to be able to automatically connect and control a remote computer over the internet without having to configure the router it's connected to. Does Apple Remote Desktop have this capability?
Apple Remote Desktop will involve either having a VPN or open ports and static IPs. I think you will be much better off with LogMeIn.com's free version, which will require zero intraction from your family members and open ports are not necessary. You will need to know a user's credentials on their computer. If they require more privacy they can disable LogMeIn from the menu bar item, as it will always be on as long as they are connected to the Internet. I suggest adding a user to each computer with your name and one password—that will be one less thing for you to remember and if they change their password or don't remember it you can still help them. 

I use both ARD and LogMeIn daily, but ARD is more than you need.