DateTime.ToString("MM/dd/yyyy HH:mm:ss.fff") resulted in something like "09/14/2013 07.20.31.371"

Is it because some culture format issue?

Yes. Your user must be in a culture where the time separator is a dot. Both ":" and "/" are interpreted in a culture-sensitive way in custom date and time formats.

How can I make sure the result string is delimited by colon instead of dot?

I'd suggest specifying CultureInfo.InvariantCulture:

string text = dateTime.ToString("MM/dd/yyyy HH:mm:ss.fff",
                                CultureInfo.InvariantCulture);

Alternatively, you could just quote the time and date separators:

string text = dateTime.ToString("MM'/'dd'/'yyyy HH':'mm':'ss.fff");

... but that will give you "interesting" results that you probably don't expect if you get users running in a culture where the default calendar system isn't the Gregorian calendar. For example, take the following code:

using System;
using System.Globalization;
using System.Threading;

class Test
{
    static void Main()        
    {
        DateTime now = DateTime.Now;
        CultureInfo culture = new CultureInfo("ar-SA"); // Saudi Arabia
        Thread.CurrentThread.CurrentCulture = culture;
        Console.WriteLine(now.ToString("yyyy-MM-ddTHH:mm:ss.fff"));
    }
} 

That produces output (on September 18th 2013) of:

11/12/1434 15:04:31.750

My guess is that your web service would be surprised by that!

I'd actually suggest not only using the invariant culture, but also changing to an ISO-8601 date format:

string text = dateTime.ToString("yyyy-MM-ddTHH:mm:ss.fff");

This is a more globally-accepted format - it's also sortable, and makes the month and day order obvious. (Whereas 06/07/2013 could be interpreted as June 7th or July 6th depending on the reader's culture.)

: has special meaning: it is The time separator. (Custom Date and Time Format Strings).

Use \ to escape it:

DateTime.ToString(@"MM/dd/yyyy HH\:mm\:ss.fff")

Or use CultureInfo.InvariantCulture:

DateTime.ToString("MM/dd/yyyy HH:mm:ss.fff", CultureInfo.InvariantCulture)

I would suggest going with the second one, because / has special meaning as well (it is The date separator.), so you can have problems with that too.

You can use InvariantCulture because your user must be in a culture that uses a dot instead of a colon:

DateTime.ToString("MM/dd/yyyy HH:mm:ss.fff", CultureInfo.InvariantCulture);