The Eiger. The name means "Ogre" in German and it has a a fearsome reputation - the brilliant book "the White Spider" probably put more people off alpinism than any other!
Climbing the Mittellegi ridge is more technical than the Matterhorn Hornli or Italian routes. The hardest parts have fixed rope, but there's still lots of climbing on flat or slopey limestone holds needing good balance and confident footwork, and some very narrow, exposed snow ridges. It starts literally as you step off the hut terrace - the lights of Grindelwald shining over 2000m below you - and is sustained all the way to the Sudliches Eigerjoch around 8 hours later.