Can anyone suggest or recommend a great online/hosted calendar system that is, hopefully, free, but if not then less than $10 per month? Anything other than Google? Must be accessible via any web browser.
I like Google Calendar, calendar.google.com. Free, fast and pretty good usability.
Windows Vista, OSX, and Ubuntu all come with calendar applications. And for more features, there is always Outlook and it's open-source clones.
I only mention this because you aren't very specific about the kind of calendar application you are looking for. How about listing features that are required and features that would be nice? The better your question is the better the answers you will get. (Generally)
I personally like Google Calendar and I love it about 10x more than I previously did because they enabled CalDAV support. CalDAV is a read/write protocol that Apple's iCal supports, which means I can do two-way sync's natively from iCal and the Web and anything else that supports CalDAV (there are plugins for most major calendar clients).
You can setup a standard WebDAV server and it will synchronize with Office Vista, Mozilla Sunbird, Mac OS X iCal, and many Linux applications. Most 3rd party web hosts offer WebDAV support, too--so you aren't locked into any particular vendor (ala Google Calendar, et all).
Chandler Hub — an instance of Chandler Server a.k.a. Cosmo, hosted by the Internet Systems Consortium.
Chandler Hub is a public service of the Open Source Applications Foundation.
If you're interested in the architecture, see http://chandlerproject.org/Developers/WebHome in particular http://chandlerproject.org/Projects/CosmoArchitecture.
Chandler Server CalDAV service includes support for VTODO. When I last checked, this was missing from Google Calendar.