We have the seven highest summits, the highest peak on each continent. Then we have Mount Kea, the highest point in Hawaii, at 10,100 m or 33,100 ft —more than twice Mount Everest‘s base-to-peak height of 3,650 to 4,650 metres (11,980 to 15,260 ft.) Across the solar system, astronomers have been calculating the high-points of every planet for decades.
The largest mountain out there is Olympus Mons on Mars. It is 21.9 km high and was discovered in 1971. Other large peaks on Mars are Ascraeus Mons at 14.9 km high and Elysium Mons at 12.6 km high. Check out this image comparing Olympus to Everest:
On the surface of Jupiter’s moon, lo, 135 mountains have been named. The largest is Boosaule Montes South at 18.2 km high. Saturn’s satellite, Lapetus, has an equatorial ridge which is 20 km high and 1,300 km long. On Venus it is Maxwell Montes at 6.4 km high and on Mercury it is Caloris Montes at only 3 km.
Lots of first ascents to be had out there.