I'm looking for an online system to manage recurring tasks,
specifically people I need to contact.  For instance, it might be
something like the following:

-Call Parents once a week
-Have lunch with Steve once a month
-E-mail Mary once every six months

I know that I could do this through Outlook but I don't want to
clutter up my Tasks there anymore.  I know there are a bunch of online
calendaring apps out there and I'm guessing one of them might have
this capability (although I haven't found one yet that does).  I don't
want to install anything more on my computer if at all possible and
ideally something like this would be free or fairly cheap.

Does anyone have any suggestions?

You can opt to use Office 2003 Live there is a way of using Outlook
2003 remotely. This is the link where I found information.

http://office.microsoft.com/en-us/assistance/HA100662331033.aspx

I'm having the same issue, I need to get my emails, tasks, contacts,
etc. where I go, so I'm planning to buy for myself a GPRS/GSM/EDGE/
G3(optional) compatible PocketPC. This way I have access to the
internet so I can recieve and answer emails and I can manage my tasks,
to do list, contacts and even sms and mms messenges from any place
with WIFI, Bluetooth or GPRS/EDGE/G3 signal.

There is a very wide range of prices, a good choice would be the KJAM
IMATE or the QTEC 9100, they are portable and they have a sliding
keyboard to make it easy to input data.

Hope this info has helped you.

Best regards,
RelativeInsanity