Generate random numbers without repetitions
Updated answer in response to bounty: See Is that your final answer? at the end, and other changes - basically answer is significantly rewritten.




To break your problem down in to requirements:


you need a set of random numbers
the numbers need to be unique
the order of the returned numbers needs to be random


Your current code indicates that the range of random numbers is specified by Random.Next(), which returns values in the [0 .. Int32.MaxValue) range (note, it excludes Int32.MaxValue). This is significant for the purpose of this question, because other answers have assumed that the range is configurable, and 'small'.

If the range should be configurable, then the recommended algorithm would potentially be much larger.

Based on those assumptions, let's do a code review...

Code Style

do ... while

The most glaring problems here are the un-braced do-while loop. You already knew it, but this code is ugly:


    do number = random.Next();
    while (randomNumbers.Contains(number));



It really should be braced:

    do
    {
        number = random.Next();
    } while (randomNumbers.Contains(number));


This makes the statement clear, and significantly reduces confusion. Always use braces for 1-liners.

List Construction

The List class allows an initial capacity to be used. Since the capacity needs to just be count, it makes sense to initialize the list with this capacity:

List&lt;int&gt; randomNumbers = new List&lt;int&gt;(count);


Current Algorithm

This is where the most interesting observations can be made. Let's analyze your current algorithm:


Create a container for the results
repeat until you have selected N values:

Select a random value
check if it has been previously selected
if it is 'new', then add it to the container



This algorithm will produce random values, in a random order, and with good random characteristics (no skews, biases, gaps, etc.).

In other words, your results are good.

The problem is with performance....

There are two performance concerns here, one small, the other large:


the do-while loop to avoid collisions
the List container


do-while performance

The do-while has a very low impact on performance... almost negligible. This is hotly debated, but, the reality is that you would need a very, very large count before this becomes a problem. The reasoning is as follows:

Collisions happen when the random value was previously selected. For the specified range of [0 .. Int32.MaxValue), you would need a very large count before collisions actually happened. For example, count would have to be about 65,000 before there was better than a 50% chance that there was even a single collision.

In a general sense, given a Range of \$N\$, select \$M\$ numbers. If \$M &lt; \sqrt{N}\$ then the probability of a single collision is &lt; 50%. Since the Range is very large, the probability is small.

Obviously, if the range was small, then the probabilities would be significantly affected. But the range is fixed at Int32.MaxValue, so that's OK.

Additionally, if the count was large, then the probabilities would also be affected. How large would be very large? Well, you would be running in to very large arrays before you run in to significant problems..... I would venture you are hitting close to \$\frac{Int32.MaxValue}{2}\$ before you run in to a significant issue with performance.

List performance

This is without doubt your largest concern. You use the randomNumbers.Contains(number) call to determine whether a value was previously selected. This requires a scan of all previously-selected values to determine. As mentioned, this will almost always return false, and will thus have to scan the entire list.

As the count value increases, the length of time to perform the Contains will increase at an quadratic rate, \$O(n^2)\$ where n is count.

This performance problem will become critical much sooner than the random-collision problem.

Putting it together

The problem you have in your code is that you are trying to do too much at once, you are using a List because that is your return value, when a HashSet would be better. If you break the problem down in to stages, you will be able to solve things more elegantly.

If you add a duplicate value to a HashSet, it does not grow, and the operation performance is not dependent on the amount of data in the HashSet (it is \$O(1)\$). You can use the Count of the HashSet to manage the data uniqueness.

Once you have a clean set of unique random numbers, you can dump them in to a List, then shuffle the list using an efficient shuffle.

Combining these data structures, in the right way, leads to an overall \$O(n)\$ solution, which will scale fairly well.

Here is some code, which works in Ideone too. Note, my C# is weak, so I have tried to make the logic clear.

using System;
using System.Collections.Generic;

public class Test
{
    static Random random = new Random();

    public static List&lt;int&gt; GenerateRandom(int count)
    {
        // generate count random values.
        HashSet&lt;int&gt; candidates = new HashSet&lt;int&gt;();
        while (candidates.Count &lt; count)
        {
            // May strike a duplicate.
            candidates.Add(random.Next());
        }

        // load them in to a list.
        List&lt;int&gt; result = new List&lt;int&gt;();
        result.AddRange(candidates);

        // shuffle the results:
        int i = result.Count;  
        while (i &gt; 1)
        {  
            i--;  
            int k = random.Next(i + 1);  
            int value = result[k];  
            result[k] = result[i];  
            result[i] = value;  
        }  
        return result;
    }
    public static void Main()
    {
        List&lt;int&gt; vals = GenerateRandom(10);
        Console.WriteLine("Result: " + vals.Count);
        vals.ForEach(Console.WriteLine);
    }
}


The above code is my initial recommendation, and it will work well, and scale well for any reasonable number of values to return.

Second Alternate Algorithm

The problem with the above algorithm is threefold:


When count is very large, the probability of collision is increased, and performance may be affected
Data will need to be in both the HashSet and the List at some point, so the space usage is doubled.
The shuffle at the end is needed to keep the data in a random order (HashSet does not keep the data in any specific order, and the hashing algorithm will cause the order to become biased, and skewed).


These are only performance issues when the count is very large. Note that only the collisions at large count will impact the scalability of the solution (at large count it is no longer quite \$O(n)\$, and it will be come progressively worse when count approaches Int32.MaxValue. Note that in real life this will not likely ever happen.... and memory will become a problem before performance does.

@JerryCoffin pointed to an alternate algorithm  from Bob Floyd, where a trick is played to ensure that collisions never happen. This solves the problem of scalability at very large counts. It does not solve the need for both a HashSet and a List, and it does not solve the need for the shuffle.

The algorithm as presented:


initialize set S to empty
for J := N-M + 1 to N do
    T := RandInt(1, J)
    if T is not in S then
        insert T in S
    else
        insert J in S



assumes that RandInt(1, J) returns values inclusive of J.

To understand the above algorithm, you need to realize that you choose a random value from a range that is smaller than the full range, and then after each value, you extend that to include one more. In the event of a collision, you can safely insert the max because it was never possible to include it before. 

The chances of a collision increase at the same rate that the number of values decreases, so the probability of any one number being in the result is not skewed, or biased.

Is this almost a final answer? No

So, using the above solution, in C#, would look like (in Ideone) (note, code is now different to Ideone):

public static List&lt;int&gt; GenerateRandom(int count)
{
    // generate count random values.
    HashSet&lt;int&gt; candidates = new HashSet&lt;int&gt;();
    for (Int32 top = Int32.MaxValue - count; top &lt; Int32.MaxValue; top++)
    {
        Console.WriteLine(top);
        // May strike a duplicate.
        if (!candidates.Add(random.Next(top + 1)))
        {
            candidates.Add(top);
        }
    }

    // load them in to a list.
    List&lt;int&gt; result = candidates.ToList();

    // shuffle the results:
    int i = result.Count;  
    while (i &gt; 1)
    {  
        i--;  
        int k = random.Next(i + 1);  
        int value = result[k];  
        result[k] = result[i];  
        result[i] = value;  
    }  
    return result;
}    


Note that you need to shuffle the results still, so that the HashSet issue is resolved. Also note the need to do the fancy loop-condition top &gt; 0 because at overflow time, things get messy.

Can you avoid the shuffle?

So, this solves the need to do the collision loop, but, what about the shuffle. Can that be solved by maintaining the HashSet and the List at the same time. No! Consider this function(in Ideone too):

public static List&lt;int&gt; GenerateRandom(int count)
{
    List&lt;int&gt; result = new List&lt;int&gt;(count);

    // generate count random values.
    HashSet&lt;int&gt; candidates = new HashSet&lt;int&gt;();
    for (Int32 top = Int32.MaxValue - count; top &lt; Int32.MaxValue; top++)
    {
        // May strike a duplicate.
        int value = random.Next(top + 1);
        if (candidates.Add(value))
        {
            result.Add(value);
        }
        else
        {
            result.Add(top);
            candidates.Add(top);
        }
    }

    return result;
}


The above answer is never going to allow the first value in the result to have any of the Max - Count to Max values (because there will never be a collision on the first value, and the range is not complete at that point), and this is thus a broken random generator.

Even with this collision-avoiding algorithm, you still need to shuffle the results in order to ensure a clean bias on the numbers.



TL;DR

Is This Your Final Answer? Yes!

Having played with this code a lot, it is apparent that it is useful to have a range-based input, as well as a Int32.MaxValue system. Messing with large ranges leads to potential overflows in the 32-bit integer space as well.

Working with @mjolka, the following code would be the best of both worlds:

    static Random random = new Random();

    // Note, max is exclusive here!
    public static List&lt;int&gt; GenerateRandom(int count, int min, int max)
    {

        //  initialize set S to empty
        //  for J := N-M + 1 to N do
        //    T := RandInt(1, J)
        //    if T is not in S then
        //      insert T in S
        //    else
        //      insert J in S
        //
        // adapted for C# which does not have an inclusive Next(..)
        // and to make it from configurable range not just 1.

        if (max &lt;= min || count &lt; 0 || 
                // max - min &gt; 0 required to avoid overflow
                (count &gt; max - min &amp;&amp; max - min &gt; 0))
        {
            // need to use 64-bit to support big ranges (negative min, positive max)
            throw new ArgumentOutOfRangeException("Range " + min + " to " + max + 
                    " (" + ((Int64)max - (Int64)min) + " values), or count " + count + " is illegal");
        }

        // generate count random values.
        HashSet&lt;int&gt; candidates = new HashSet&lt;int&gt;();

        // start count values before max, and end at max
        for (int top = max - count; top &lt; max; top++)
        {
            // May strike a duplicate.
            // Need to add +1 to make inclusive generator
            // +1 is safe even for MaxVal max value because top &lt; max
            if (!candidates.Add(random.Next(min, top + 1))) {
                // collision, add inclusive max.
                // which could not possibly have been added before.
                candidates.Add(top);
            }
        }

        // load them in to a list, to sort
        List&lt;int&gt; result = candidates.ToList();

        // shuffle the results because HashSet has messed
        // with the order, and the algorithm does not produce
        // random-ordered results (e.g. max-1 will never be the first value)
        for (int i = result.Count - 1; i &gt; 0; i--)
        {  
            int k = random.Next(i + 1);  
            int tmp = result[k];  
            result[k] = result[i];  
            result[i] = tmp;  
        }  
        return result;
    }

    public static List&lt;int&gt; GenerateRandom(int count)
    {
        return GenerateRandom(count, 0, Int32.MaxValue);
    }