What is the industry standard, or even just the most popular, *Online*
Project Management application?

I'm currently using NetOffice, http://netoffice.sourceforge.net/,
which judging from their activity is not the industry standard.

I have been in IT for 20 years, lately the only ones I have used are
Microsoft Project 2000 Professional  
Microsoft Project 2003 Professional  
 
http://www.microsoft.com/office/project/prodinfo/default.mspx

Keith
http://internethelp.bravehost.com

Keith,
Have you used the portion which allows you to access the information
online--Project Server, I believe? What do you think of it?

You need to look at a few different aspects.  For managing a schedule
Microsoft Project is the most common.  There are high level tools such
as Primavera and Artemis but these are mainly used for things like
building commercial offices.
The second part is all the other things you need to project manage
such as issues, risks, documents, scope variations, action items,
budget and expenditure etc.  You can buy a range of tools or something
like "Project Administrator" from Project Perfect
www.projectperfect.com.au

We host software projects at http://www.Projxpert.com/ but the
software is quite flexible. It allows your team to communicate and
collaborate around a project, no matter where they are.

You get:
 o) your own version control repository which is like having a shared
hard drive which remembers every change to every file.
 o) an issue tracker  
 o) discussion forums

The software is aimed at software developers but depending on your
requirements it could provide what your after.

s.