In reply to Removed UserAnAspiringClimber:
Not sure there are many 'last great problems' left in the Alps, unfortunately. Mainly it's a case of freeing routes that have established aid sections or massive link-ups. There's still new routing to be had, it seems (look at Matt Helliker and Jon Bracey, for example) but the new lines aren't big imposing challenges that shrug off attempt after attempt.
In the Himalaya, the west faces of K2 and Makalu are, as far as I'm aware, yet to see a successful alpine style ascent. The south face of Lhotse is a controversial one - I think it's been seiged by the Russians and Tomo Cesen claims to have soloed it but there are quite a few experienced Himalayan climbers who doubt his story.
Good thread on it here, though a bit dated (e.g. includes the Mazeno Ridge):
http://www.ukclimbing.com/forums/t.php?t=52525&v=1#x697104Post edited at 23:00