Credit card numbers are full of magic. First of all not every 16 digit is CC number, but only by number you can know the issuer. So no need to place on the web form "Visa" / "MasterCard" radio button. Ok, so what's interesting. I found two great articles that helped me with this:
http://www.merriampark.com/anatomycc.htm and http://www.beachnet.com/~hstiles/cardtype.html .

And what now ? I just finished small helper class to validate Credit Cards. Here is the source.

[code=csharp]public enum CCType
    {
        VISA, MC
    }

    /// <summary>
    /// Credit card validation.
    /// Supports : VISA and MasterCard
    /// Reference: http://www.merriampark.com/anatomycc.htm
    /// Contains LUHN (mod 10) check
    /// by D.S.
    /// http://aspnetcafe.com
    /// </summary>
    public class CreditCardValidator
    {
        protected string _CardNumber = "";

        public CreditCardValidator(string aCardNumber)
        {
            _CardNumber = aCardNumber.Replace(" ","").Replace("-","");
            ProcessValidation();
        }

        protected bool _IsValid;

        public bool IsValid
        {
            get { return _IsValid; }
            set { _IsValid = value; }
        }

        private CCType _CardType;

        public CCType CardType
        {
            get { return _CardType; }
            set { _CardType = value; }
        }
       
        protected void ProcessValidation()
        {
            bool passRegEx = false;
            bool passIssuer = false;
            bool passLuhn = false;
            IsValid = false;

            do
            {
                // Reg Ex check //
                Regex RegExNumber = new Regex(@"(?<firsttwo>(?<firstone>\d)\d)\d{11,14}");
                Match m = RegExNumber.Match(_CardNumber);
                passRegEx = m.Success;
                if (!passRegEx) break;
                string number = m.Groups[0].Value; // only digits //
                string firstNum = m.Groups["firstone"].Value;
                int firstTwoNum = int.Parse(  m.Groups["firsttwo"].Value );
                passIssuer = (firstNum == "4") || ((firstTwoNum >= 51) && (firstTwoNum <= 55));
                if (!passIssuer) break;
                if (firstNum == "4") CardType = CCType.VISA;
                if ((firstTwoNum >= 51) && (firstTwoNum <= 55)) CardType = CCType.MC;
                // Now make Luhn check //
                passLuhn = LuhnCheck(number);
                if (!passLuhn) break;
                //
                IsValid = true;
            } while (false);          
        }

        /// <summary>
        /// Performs mod 10 check
        /// </summary>
        /// <param name="cardNumber">Card Number with only numbers</param>
        /// <returns></returns>
        protected bool LuhnCheck(String cardNumber)
        {
            int sum = 0;
            int digit = 0;
            int addend = 0;
            bool timesTwo = false;

            for (int i = cardNumber.Length - 1; i >= 0; i--)
            {
                digit = int.Parse(cardNumber.Substring(i, 1));
                if (timesTwo)
                {
                    addend = digit * 2;
                    if (addend > 9)
                    {
                        addend -= 9;
                    }
                }
                else
                {
                    addend = digit;
                }
                sum += addend;
                timesTwo = !timesTwo;
            }

            int modulus = sum % 10;
            return (modulus == 0);
        }
    }[/code]

The code is quite simple. But works good for me. I'm not providing you with a sample application, you know there are my credit card number :)

Check the articles at the top of the page if you want to know how it's works. And what is Mod 10 check.