Just adding the solution I worked on this morning.
var regex = new Regex("(?<=^|,)(\"(?:[^\"]|\"\")*\"|[^,]*)");
foreach (Match m in regex.Matches("<-- input line -->"))
{
var s = m.Value;
}
As you can see, you need to call regex.Matches() per line. It will then return a MatchCollection with the same number of items you have as columns. The Value property of each match is, obviously, the parsed value.
This is still a work in progress, but it happily parses CSV strings like:
2,3.03,"Hello, my name is ""Joshua""",A,B,C,,,D