Generating random, unique values C#

I'm calling NewNumber() regularly, but the problem is I often get repeated numbers.

Random.Next doesn't guarantee the number to be unique. Also your range is from 0 to 10 and chances are you will get duplicate values. May be you can setup a list of int and insert random numbers in the list after checking if it doesn't contain the duplicate. Something like:

public Random a = new Random(); // replace from new Random(DateTime.Now.Ticks.GetHashCode());
                                // Since similar code is done in default constructor internally
public List<int> randomList = new List<int>();
int MyNumber = 0;
private void NewNumber()
{
    MyNumber = a.Next(0, 10);
    if (!randomList.Contains(MyNumber))
        randomList.Add(MyNumber);
}

You might try shuffling an array of possible ints if your range is only 0 through 9. This adds the benefit of avoiding any conflicts in the number generation.

var nums = Enumerable.Range(0, 10).ToArray();
var rnd = new Random();

// Shuffle the array
for (int i = 0;i < nums.Length;++i)
{
    int randomIndex = rnd.Next(nums.Length);
    int temp = nums[randomIndex];
    nums[randomIndex] = nums[i];
    nums[i] = temp;
}

// Now your array is randomized and you can simply print them in order
for (int i = 0;i < nums.Length;++i)
    Console.WriteLine(nums[i]);

NOTE, I dont recommend this :). Here's a "oneliner" as well:

//This code generates numbers between 1 - 100 and then takes 10 of them.
var result = Enumerable.Range(1,101).OrderBy(g => Guid.NewGuid()).Take(10).ToArray();