Not just a building, even a working clock :).

The Long Now foundations 10,000 year clock is designed to last for 10,000 years.

Quote from this first video "I'm very optimistic about the future. I'm not optimistic because I think our problems are small, I'm optimistic because i think our capacity to deal with problems are great"

It ticks once a year.

“There is a Clock ringing deep inside a mountain. It is a huge Clock, hundreds of feet tall, designed to tick for 10,000 years. Every once in a while the bells of this buried Clock play a melody. Each time the chimes ring, it’s a melody the Clock has never played before. The Clock’s chimes have been programmed to not repeat themselves for 10,000 years. Most times the Clock rings when a visitor has wound it, but the Clock hoards energy from a different source and occasionally it will ring itself when no one is around to hear it. It’s anyone’s guess how many beautiful songs will never be heard over the Clock’s 10 millennial lifespan.”

It’s powered by sunlight.

“Behind the main chamber’s dials the stairs continue up to the outside summit of the mountain. The shaft above Clock continues to the surface, where its opening to the daylight is capped with a cupola of sapphire glass. This is the only part of the clock visible from outside, on the mountain peak. In this outdoor cupola sits the thermal-difference device to power the timekeeping, and also a solar synchronizer. Every sunny noon, a prism directs sunlight down the shaft and slightly heats up this ingenious mechanical device. That synchronizing signal is transmitted by rods further down to the Clock’s innards, where the imperceptible variations in the length of the day as the earth wobbles on its axis will be compensated so that the Clock can keep its noon on true solar noon. In that way the Clock is self-adjusting, and keeps good time over the centuries.”

It uses ceramic bearings, which can run without lubrication.

For more details, see Introduction - 10,000 Year Clock - The Long Now