How to take all but the last element in a sequence using LINQ?

I don't know a Linq solution - But you can easily code the algorithm by yourself using generators (yield return).

public static IEnumerable<T> TakeAllButLast<T>(this IEnumerable<T> source) {
    var it = source.GetEnumerator();
    bool hasRemainingItems = false;
    bool isFirst = true;
    T item = default(T);

    do {
        hasRemainingItems = it.MoveNext();
        if (hasRemainingItems) {
            if (!isFirst) yield return item;
            item = it.Current;
            isFirst = false;
        }
    } while (hasRemainingItems);
}

static void Main(string[] args) {
    var Seq = Enumerable.Range(1, 10);

    Console.WriteLine(string.Join(", ", Seq.Select(x => x.ToString()).ToArray()));
    Console.WriteLine(string.Join(", ", Seq.TakeAllButLast().Select(x => x.ToString()).ToArray()));
}

Or as a generalized solution discarding the last n items (using a queue like suggested in the comments):

public static IEnumerable<T> SkipLastN<T>(this IEnumerable<T> source, int n) {
    var  it = source.GetEnumerator();
    bool hasRemainingItems = false;
    var  cache = new Queue<T>(n + 1);

    do {
        if (hasRemainingItems = it.MoveNext()) {
            cache.Enqueue(it.Current);
            if (cache.Count > n)
                yield return cache.Dequeue();
        }
    } while (hasRemainingItems);
}

static void Main(string[] args) {
    var Seq = Enumerable.Range(1, 4);

    Console.WriteLine(string.Join(", ", Seq.Select(x => x.ToString()).ToArray()));
    Console.WriteLine(string.Join(", ", Seq.SkipLastN(3).Select(x => x.ToString()).ToArray()));
}

Because I'm not a fan of explicitly using an Enumerator, here's an alternative. Note that the wrapper methods are needed to let invalid arguments throw early, rather than deferring the checks until the sequence is actually enumerated.

public static IEnumerable<T> DropLast<T>(this IEnumerable<T> source)
{
    if (source == null)
        throw new ArgumentNullException("source");

    return InternalDropLast(source);
}

private static IEnumerable<T> InternalDropLast<T>(IEnumerable<T> source)
{
    T buffer = default(T);
    bool buffered = false;

    foreach (T x in source)
    {
        if (buffered)
            yield return buffer;

        buffer = x;
        buffered = true;
    }
}

As per Eric Lippert's suggestion, it easily generalizes to n items:

public static IEnumerable<T> DropLast<T>(this IEnumerable<T> source, int n)
{
    if (source == null)
        throw new ArgumentNullException("source");

    if (n < 0)
        throw new ArgumentOutOfRangeException("n", 
            "Argument n should be non-negative.");

    return InternalDropLast(source, n);
}

private static IEnumerable<T> InternalDropLast<T>(IEnumerable<T> source, int n)
{
    Queue<T> buffer = new Queue<T>(n + 1);

    foreach (T x in source)
    {
        buffer.Enqueue(x);

        if (buffer.Count == n + 1)
            yield return buffer.Dequeue();
    }
}

Where I now buffer before yielding instead of after yielding, so that the n == 0 case does not need special handling.