The defined "Kármán line" at 100 km (62.14 mi) is actually not the true one. The true line Theodore of Kármán mentioned was at 57 mi / 91.5 km. Eventually, Kármán and the FAI just took the nextmost double-0-value in metric units which is 100 km and defined that as the "Kármán line". However, 57 miles are also a bit too high. Uhoh determined what is considered the Kármán line should actually be at 50 mi (80.5 km) which is the U.S.-defined space border and around the mesopause (meso-/thermosphere border).
So on Earth, outer space begins at the mesopause at around 50 mi (80.5 km).
As for other planets and moons, it depends on how high the atmosphere reaches which is not necessarily conclusive from the surface air pressure. Martian surface pressure is analogous to that of the Earth's stratosphere, the locations that have the highest air pressure (0.012 atm) are like about 19 mi (30 km) above the Earth's surface. I don't know well how high it reaches but Mark Adler already told you that it are obviously 88 km (54.7 mi).
So on Mars it's 54.7 mi (88 km) and thus higher than on Earth despite the surface pressure being lower than the Earth's.
The atmosphere of Venus (surface pressure: 91.8 atm) reaches very high, up to 200-250 mi (320-400 km).
And the atmosphere of Titan (surface pressure: 1.45 atm) reaches even higher, up to 300-400 mi (480-640 km).
The four gas planets consist only of gas except a likely core (Saturn however has no solid core) so you can only consider an altitude of the atmosphere either from the core's surfaces (the cores are about as big as the entire planet Earth) or from what is defined as Earth-like atmospheric pressure level so the altitude at which space begins may be similar to that on the Earth.
Neptunian moon Triton and the "dwarf planets" Pluto and Eris have a surface air pressure similar to that in the Earth's mesosphere (around 1 Pa) from which we may conclude that it's not very high, however Pluto's atmosphere indeed is, I however dunno how high exactly. Perhaps Earth-like.
Jupiter's moon Io has has an atmospheric pressure of up to 40 nbar in certain locations close to volcanoes. All of Io's collisional atmosphere reaches quite high too (perhaps as high as the Earth's space border) but such high pressure rather is found at those locations only.
Question on space border and uhoh's answer to it