string clipboardTextBefore = "";

private void clipboardwatchtimer_Tick(object sender, EventArgs e){
if (Clipboard.ContainsText()) {
string clipboardTextAfter = (Clipboard.GetText());
if (clipboardTextAfter != clipboardTextBefore)
{textBox1.Text = clipboardTextAfter;
clipboardTextBefore = clipboardTextAfter}
}}

こうじゃないかな
タイマーの中でThread.Sleepとかやらん方がいいと思うよ