You should know most of these, but hit the links for more details.
1. We don't know the Doctor's name.
It isn't Doctor Who, but it isn't necessarily wrong to call him that.
2. The Doctor fought the Nestene and the Autons.
In fact the Third Doctor faced them twice.
3. The Doctor's age is hard to pin down.
He's a time traveler, it's difficult to keep track.
4. The Doctor fought the Daleks.
5. The Doctor is probably an actual doctor.
But possibly not.
6. The Doctor regenerated many times.
And it was often very different.
7. The Doctor fought the Master.
And sometimes they even worked together.
8. The Doctor fought the Cybermen.
Almost as much as he fought the Daleks.
9. The Doctor traveled with Sarah Jane Smith.
Especially the Third and Fourth Doctors.
10. The Doctor traveled with K9.
Actually more than one.