VS.NET when used with web / asp projects can't handle the .svn folders that Subversion uses to store its internal information. This is not a bug in Subversion. The bug is in Visual Studio and the frontpage extensions it uses. Even though you might argue that Windows can't handle such foldernames, it's not correct. Windows can handle such folders very well, you just can't create them with the explorer.
The error message you most likely will get in VS.NET2003 is "Refreshing the project failed. Unable to retrieve folder informatin from the server."
As of Version 1.3.0 of Subversion and TortoiseSVN, you can set the environment variable SVN_ASP_DOT_NET_HACK. If that variable is set, then Subversion will use _svn folders instead of .svn folders. You must restart your your shell for those env variable to take effect
However, this bug applies only when you use web projects, which is not the same as ASP.NET projects. Usually, when you want to create an ASP.NET project, you choose to create a web project. But you can create or convert an ASP.NET project as a class project. With some minor tweaking, you won't notice the difference, and you then can use TortoiseSVN and SVN with .svn folders without problems.
There is a really good blog post that helps you to convert your ASP.NET web projects to ASP.NET class project. You can find it here: http://www.pluralsight.com/fritz/Samples/aspdotnet_without_web_projects.htm
If you follow those instructions, you'll have a VS.NET working with ASP.NET projects and Subversion without troubles.
Alternatively, upgrade your copy of VS.NET. The bug has been fixed in VS.NET2005, so it no longer has this problem.