Yes, other planets have oxygen.
Here is the amount of oxygen in the atmospheres of the 8 planets:
- Mercury: 42% oxygen
- Venus: negligible
- Earth: 21% oxygen
- Mars: 0.13% oxygen
- Jupiter: negligible
- Saturn: negligible
- Uranus: negligible
Now, Mercury has a very high atmospheric content of oxygen, but its atmosphere is VERY thin. While the Earth’s atmosphere at sea level is 1 bar, the trace atmosphere on Mercury is 0.00000000000001 bars (1x10^-13 bars). Not enough for the capacity of the human lungs.
One of the reason why atmospheric oxygen is in such a trace amount is that there are very little natural inorganic reactions that can produce free oxygen. Because it’s highly reactive, oxygen tend to exist with other elements. Most of the oxygen on our planet is considered to be attributed to the process of photosynthesis, which is absent on the other planets as it requires the existence of life.
Source: Planetary Atmospheres