In my experience, web.config files are widely reviled. In particular, I have found them difficult to manage when you have multiple environments to support, and fiddly to update due to the lack of validation at update-time and the verbosity of XML.
What are the alternatives?
How long has ASP.NET been in existence; how many production web sites are using it?
They're almost all using web.config, as it comes, out of the box. They can't be "reviling" it too much.
That said, look at the new features of ASP.NET in .NET 4.0, including configuration-specific web.config files, and xml-based transformations of web.config that permit environment-specific web.config versions to be generated at deployment time.
You may revile that a little less.
I strongly disagree with your assertion that web.config files are "widely reviled." In my experience, they're easy to maintain and manage, and in some cases are the only place you can put configuration data.
It's worth noting that VS2010 supports per-build configuration web.config transforms. I have a web.config, web.debug.config, and web.release.config. The debug and release files override the connection strings specified in web.config and replace them with the correct strings, for my debug and production SQL Servers, specifically. I'm also using this to make some AppSettings values config-specific.
Since you can add a build config for as many different targets or configurations as you require, I don't see why you'd feel the need to reinvent the wheel by devising another repository.
That said, you can use just about any repository for whatever data you want to store. A database, text config file of the format of your choice, encrypted image, or what have you.
I'm tempted to ask your name and employer so that, if you wind up going this route, I won't wind up maintaining such ill-conceived code in the future.