Any area, mountain range, country in particular you're curious about? It's a big world out there.

Some of the favorite climbs/summits I have done:

Ancient Art in Utah
South Six Shooter in Utah
Nevado Tolima in Colombia
Antisana in Ecuador
Puccacaca in Peru
North Face Romsdalshorn in Norway
Steger Route on the First Sella Tower in the Dolomites/Italy
Chhukhung in Nepal (for the views; the peak itself is just a scramble)
Mt. Meru in Tanzania (because of the wildlife)
Gunung Leasur on Sumatra in Indonesia (because of the scenery and wildlife)

My personal list will be limited by the fact that I am neither an alpine climber or a technical rock climber or canyoneer, but a hiker mostly who is stretched at any scrambling beyond class 3. But I enjoy a good stretching of my abilities – and not just distance or climbing skill – but also in planning and getting to the start of the ascent and route finding along the way. That the ascent be wild and uncrowded is assumed.

For Mountains – Physical Challenge (For me)
Banner Peak (First real mountain)
Mount Tukuhnikivatz
Fern’s Nipple
Manly Beacon
Higher Catedral Rock

Mountains - Research Challenge
Cloud Splitter
Sleeping Giant (Ontario)

Mountains – Winter Snowshoe Challenge
Hogback Mountain
Mount Trudee

Canyon Hikes
Zion Narrows
Kadunce Canyon
Indian Canyon