How do I check if a given string is a legal/valid file name under Windows?

You can get a list of invalid characters from Path.GetInvalidPathChars and GetInvalidFileNameChars.

UPD: See Steve Cooper's suggestion on how to use these in a regular expression.

UPD2: Note that according to the Remarks section in MSDN "The array returned from this method is not guaranteed to contain the complete set of characters that are invalid in file and directory names." The answer provided by sixlettervaliables goes into more details.

For .Net Frameworks prior to 3.5 this should work:

Regular expression matching should get you some of the way. Here's a snippet using the System.IO.Path.InvalidPathChars constant;

bool IsValidFilename(string testName)
{
    Regex containsABadCharacter = new Regex("[" 
          + Regex.Escape(System.IO.Path.InvalidPathChars) + "]");
    if (containsABadCharacter.IsMatch(testName)) { return false; };

    // other checks for UNC, drive-path format, etc

    return true;
}

For .Net Frameworks after 3.0 this should work:

http://msdn.microsoft.com/en-us/library/system.io.path.getinvalidpathchars(v=vs.90).aspx

Regular expression matching should get you some of the way. Here's a snippet using the System.IO.Path.GetInvalidPathChars() constant;

bool IsValidFilename(string testName)
{
    Regex containsABadCharacter = new Regex("["
          + Regex.Escape(new string(System.IO.Path.GetInvalidPathChars())) + "]");
    if (containsABadCharacter.IsMatch(testName)) { return false; };

    // other checks for UNC, drive-path format, etc

    return true;
}

Once you know that, you should also check for different formats, eg c:\my\drive and \\server\share\dir\file.ext

From MSDN's "Naming a File or Directory," here are the general conventions for what a legal file name is under Windows:

You may use any character in the current code page (Unicode/ANSI above 127), except:

• < > : " / \ | ? *
• Characters whose integer representations are 0-31 (less than ASCII space)
• Any other character that the target file system does not allow (say, trailing periods or spaces)
• Any of the DOS names: CON, PRN, AUX, NUL, COM0, COM1, COM2, COM3, COM4, COM5, COM6, COM7, COM8, COM9, LPT0, LPT1, LPT2, LPT3, LPT4, LPT5, LPT6, LPT7, LPT8, LPT9 (and avoid AUX.txt, etc)
• The file name is all periods

Some optional things to check:

• File paths (including the file name) may not have more than 260 characters (that don't use the \?\ prefix)
• Unicode file paths (including the file name) with more than 32,000 characters when using \?\ (note that prefix may expand directory components and cause it to overflow the 32,000 limit)