Through the years I have helped my friends and family sort out their Macs whenever problems arose. Honestly it hasn't been often. I always tell people, if you get a Mac I'll help you with whatever problems you encounter but if you buy a windows machine you're on your own. A tribute to how easy they are to get to do what you want that I'm rarely forced to make good on the promise ;) Recently I've been helping my sister rebuild a corrupted iPhoto library and try to figure out whats wrong with all that. Doing it via "type this, click that and read me message" sort of phone support would have been impossible and caused probably a family schism due to yelling, screen sharing is the best option. But she's in another state.
In an ancient world so old as to be mostly myth and legend there was "timbuktu" which I used a lot in those heady days alas it is no longer around.
In the only slightly less distant past there was "share my desktop" a great little VNC server that you could run as a regular app, double click and it was on and I could connect and help quit the app and it was off and no danger of leaving a service running in the background on their machines open to the internet.
Eventually Apple added VNC support directly to the system. But this doesn't really solve the problem because I'd have had to walk her through configuring her router to pass through the ports for it and setup NAT to the proper mac which would have a dynamic address so it would eventually stop working and so I've have to setup either a DHCP reservation or a static IP for that machine and then run a dyndns or no-ip.com client so as to be able to find her IP or teach her how to read it off the router config page or something. Far too much work.
iChat still supports screen sharing, but only through AIM accounts, not through iMessage accounts. Which seems a terrible step backwards. I still can't quite believe there isn't a way to make this work, but I couldn't figure it out.
But now we have Back To My Mac, which isn't really all that hyped by Apple. It provides an IPv6 tunnel into our machines that we can access via our iCloud ID's. But it's not really setup to connect to other peoples machines at all, only to your own. Having had so much trouble with calendars and such and iCloud in the beginning the very last thing I was going to do was sign my computer out of my own iCloud account and into hers, I am a little shaky even thinking about what that would do to our photo streams and iTunes ID's and email and calendaring... yikes.
Luckily, you can just create another user temporarily to play with! I walked her through turning on and sining into iCloud on her machine. Then in the sharing panel you have to turn on both screen sharing AND file sharing even if you're not going to share files because that is the finder interface to screen sharing. (yes, you can probably use the command line to get the IPv6 dns name of the machine and use that directly into the VNC connection dialog, but you try walking a non-computer oriented family member through the command line commands to do this, no thank you ;)
I then created a temporary user on my own mac, signed into iCloud with her ID and there, right in my sidebar was her shared drive. Click it and "share screen" was available right there in the finder and I was able to sort it out.
Not exactly seamless for helping your family and friends as they still need to share more of their passwords with you than you should need to, but no software installs necessary, no external sites, no configuring the router for NAT over the phone. All in all back to my mac is a win, they need more features but it's really an awesome hidden selling point for your Mac. If you're not using it you should be!