A simple modification of the accepted answer that returns a new list instead of working in-place, and accepts the more general IEnumerable<T> as many other Linq methods do.
private static Random rng = new Random();
/// <summary>
/// Returns a new list where the elements are randomly shuffled.
/// Based on the Fisher-Yates shuffle, which has O(n) complexity.
/// </summary>
public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> list) {
var source = list.ToList();
int n = source.Count;
var shuffled = new List<T>(n);
shuffled.AddRange(source);
while (n > 1) {
n--;
int k = rng.Next(n + 1);
T value = shuffled[k];
shuffled[k] = shuffled[n];
shuffled[n] = value;
}
return shuffled;
}