What is a more unique delimiter than comma for separating strings?

The best solution is to stick to commas and introduce support for character escaping. Whatever character you select will eventually need to be entered so you may aswell provide support for this.

Think backslases + double quotes inside double quoted strings.

Don't pick a character like backtick because some users might not know how to type it in...

Will the user be entering delimited strings into the textboxes, or will they be entering individual strings which will then be built into delimited strings by your code?

In the first case it might be better to rethink your UI instead. eg, The user could enter one string at a time into a textbox and click an "Add to list" button after each one.

In the second case it doesn't really matter what delimiter you use. Choose any character you like, just ensure that you escape any other occurrences of that character.

EDIT

Since several comments on other answers are asking for code, here's a method to create a comma-delimited string, using backslash as the escape character:

public static string CreateDelimitedString(IEnumerable<string> items)
{
    StringBuilder sb = new StringBuilder();

    foreach (string item in items)
    {
        sb.Append(item.Replace("\\", "\\\\").Replace(",", "\\,"));
        sb.Append(",");
    }

    return (sb.Length > 0) ? sb.ToString(0, sb.Length - 1) : string.Empty;
}

And here's the method to convert that comma-delimited string back to a collection of individual strings:

public static IEnumerable<string> GetItemsFromDelimitedString(string s)
{
    bool escaped = false;
    StringBuilder sb = new StringBuilder();

    foreach (char c in s)
    {
        if ((c == '\\') && !escaped)
        {
            escaped = true;
        }
        else if ((c == ',') && !escaped)
        {
            yield return sb.ToString();
            sb.Remove(0, sb.Length);
        }
        else
        {
            sb.Append(c);
            escaped = false;
        }
    }

    yield return sb.ToString();
}

And here's some example usage:

string[] test =
    {
        "no commas or backslashes",
        "just one, comma",
        @"a comma, and a\ backslash",
        @"lots, of\ commas,\ and\, bac