That's what I'm looking for. It's been an interesting hunt so far, which has yielded all kinds of promising-looking possibilities, but nothing that seems perfect or even close.
So here's the journey I've been on and what I've found so far.
General observations: lots of the software/webware out there assumes that you are a business maven with clients and projects and you're on your cell 24/7 and you just want to be the best damn project manager on the planet. If you're not in this category, you get one thing--either a calendar or a to-do list, but not both (at least not of the web-based variety).
Starting points: 43 Folders and Lifehacker are fabulous resources. I found lots of interesting things to check out through them.
Calendar stuff: RSS Calendar has potential. It's got a nice, clean look. You can include the calendar in your web site easily. You can even import your calendar--and others--into your iCal. However, it doesn't go the other way. I can't import anything into--not iCal, not Palm.
Trumba is another nice-looking calendar, but it costs money eventually (not too much, mind you, but still). It does, however, allow you to import your iCal data, which is cool. You can publish it to a website or simply make your calendar public. I wish it had the javscript thingy just to include it in a website.
And you can always publish iCal to your .Mac or Webdav enabled site. But--you can't enter new events via the web. I also tried Sunbird, but it's very similar to iCal, not quite web-based.
The problem with all these (including the web-based version of iCal) is that you can't include a task list. What would be nice is a dynamically generated task list based on the date. So let's say you have tasks that are due next Monday. You have set a reminder for 3 days before the task is due, estimating that you need to spend a portion of the prior 3 days working on it. 3 days before the task is due, the task shows up at the top of the list--either to the side of the calendar or on the calendar itself.
There are some server-side calendar programs, but I don't want to go there yet. And there may be other web-based calendars that I'm not yet aware of. I looked at several more, but many were kind of creepy looking.
Tasks/To-dos, etc.: I have tried Backpackit and Ta-Da, both made by the same company, 37signals, llc. Backpackit is basically and extension of ta-da, adding the ability to add files, images (if you pay) and create kind of a web site. You can upgrade to Basecamp which is more of a full-blown project management application and not what I needed at all.
(just so you know, I have like 20 tabs open right now with all the various software I'm considering)
I also looked at Burnout Menu 2.0. Although you can export your tasks as html, it doesn't really have a web-based option.
Tasktoy was a simple task list app I found. Maybe too simple.
We use TasksPro at work--which is okay as far as it goes. I'm trying out the personal version. It looks pretty cool so far. It has a calendar though it's kind of separate from the task list. The tasks show up on the calendar and next to the calendar, but it's not seamless and it's hard to get back to the task list list from the calendar.
While I am perfectly willing to piece together what I need, pulling in a calendar from one place, a to-do list from another, and shopping lists from still another, I'm surprised there isn't a better-integrated, free or cheap task/event management system. If you're a web programmer, this could be big--big I tell you.
So, obviously, I'm still undecided. Some sticking points for me are the fact that I'm either mac or linux-based. I have a group calendar where all my appointments/meetings are scheduled that I sync with my palm. I can then sync my palm with my home ical and I don't mind importing that into a web-based program. However, I also need to be able to go the other way. If I'm in the library and suddenly need to enter a task or an event/appointment and I don't have my palm (this does actually happen to me) and I enter it on my web calendar, I need for that event to be synced--with my palm and then to my other calendars. I want everything in one place and everything in all places if that makes sense.
I'll keep you updated--and suggestions are always welcome.