In reply to rock spider:
That Wikipedia article is surprising good, given some of the crap out there, like Peakware. There was an article on this earlier this year on mounteverest.net if you want to trawl for it.
Samoilov and Urubko bailed off the N face proper and summited via the N ridge, first ascent of the route in 10 yrs, a huge effort, maybe the first true alpine-style ascent of K2.
The true west face of Makalu is still unclimbed. There was a Russian route up the right side but it avoided the main difficulty of the huge steep rock wall. Highest ever got on it was in the 80s by either Alex McIntyre or Erhard Loretan.
There's still not a route up the main part of the S face of Dhaulagiri. Humar's route traversed off and was generally overhyped, though he did some hard climbing and took a lot of risk.
Worse is the N (Kangshung) face of Lhotse - big and steep but totally covered by huge seracs. Never attempted.
Mazeno Ridge of Nanga Parbat has now been climbed, but still not to the summit. ie. significantly harder.
E face of Kanchenjunga - rarely seen, never attempted, huge. Indian route from this side was to the N of it.
E ridge of Broad Peak. Hiding in plain sight, seen by thousands, never attempted (?). SE ridge attempted at least three times, no success.
NW ridge of Dhaulagiri - long, very long, bit hard up high.
N side of Disteghil Sar. Only one attempt, everyone died.
N ridge of Shingu Charpa. One claimed ascent, everyone lied. Still not completed. Crap rock.
N face of Namche Barwa would be huge - over 3000m above the gorge. Only one ascent of the peak. Hard to get to.
Zemu is not really a mountain, from what I know of it on paper. The Kabru issue is interesting, I think it was semi-resolved, but again, the peak in question is not a stunner. Ditto Saser Kangri II etc.
Karjiang is next on the list. It's reasonably steep and more independent than the above two. Been attempted twice.
Ultar has been climbed two or three times now, but the SE (Hidden) Pillar was attempted last month by Jed Brown and Colin Haley. Fowler and Saunders first attempted it in the 90s, Bubendorfer looked at it and Graziani and Co tried it a couple of years ago. Jed and Colin didn't really get on it as it was so out of condition and weather was shit. It's 3100m high, two days from the road.
Highest unclimbed peak in the Andes is .... (really terrible rock, rarely attempted, over 5000m).
And interestingly, as far as I know not one of these objectives has ever been attempted 'for charity' ...
D