I second logmein free edition. I have it set up on literally half a dozen or more family computers, evenly split between XP, Vista and Win7. This is by far the easiest way to fix 90% of issues. The rest of the time the answer is normally to instruct them over the phone to reset the modem and/or router to fix connection issues.
You do have to tailor your usage to the family member. If they are completely computer illiterate, then setting up a separate non-administrator account is a good thing. Otherwise, particularly with Vista and later, just teach them to always say 'no' to the access control popups unless they check with you first. If you teach them safe habits, it'll be better for everyone.
For AOL, start by showing them how to use http://aol.com/ instead of the AOL software by making that the homepage on Chrome or FF. Also, try to make that icon more prevalent than the AOL software. If they don't learn, tell them that AOL software no longer exists when your finally able to get them a new computer. I've done this for 3 people already - it's not a lie if you didn't bother to check if AOL software still exists ;-)
As for other suggestions on here about Linux, that's a mixed bag. I successfully transitioned my Dad from XP to Linux for about a year or two when I cleaned his old computer. For his basic usage (email, movie listings, weather reports), it was more than adequate. The only issue I had was one exasperating series of tech support sessions with Verizon when he switched ISPs and they insisted they didn't support Linux on a 3-way conference call...eventually I got them to believe me that the modem was broken after looking up the manual and finding the non-Windows-CD configuration page...
Eventually he switched back to Windows when the computer died and he wanted something that could support certain Windows-only software. He knows not to install anything on the computer, and also tends to say no to all popups (good and bad), so I just have to explicitly run updates periodically.