private static T FindMinimum<T>(IEnumerable<T> collection, T
identityElement) where T : IComparable<T> {
  T min = identityElement;
  foreach (T t in collection) {
    if (t.CompareTo(min) < 0) min = t;
  }
  return min;
}

Sample use:

FindMinimum(new int[] { 2, 3, 1 }, Int.MaxValue) == 1
FindMinimum(new int[] { }, Int.MaxValue) == Int.MaxValue

You can leave out the "identity element" thing and restrict the function to
operate on non-empty collections only, but that's not as concise:

private static T FindMinimum<T>(IEnumerable<T> collection) where T :
IComparable<T> {
    IEnumerator<T> enumerator = collection.GetEnumerator();
    if (!enumerator.MoveNext()) throw new ArgumentException("Attempt to
find the minimum of an empty collection.");
    T min = enumerator.Current;
    while (enumerator.MoveNext()) {
      if (enumerator.Current.CompareTo(min) < 0) min = enumerator.Current;
    }
    return min;
}

It is worth mentioning that .NET 3.5 provides this functionality "out
of the box" via Enumerable.Min<T>() etc. Also, Comparer<T>.Default can
be used if you don't want to enforce the constraint in the API; while
constraints are a good thing, the downside is that it tends to
snowball, so higher up functions end up with 3 or 4 constraints that
are only used in edge-cases. This approach [Comparer<T>.Default, no
constraint] is what LINQ uses (.NET 3.5).

Marc