I am an amateur astronomer, with a small telescope.
One night, I was looking at the Andromeda galaxy, our "nearest neighbor" galaxy, if you don't count the Magellanic Clouds, which are "satellite galaxies" of the Milky Way (and only visible from the southern hemisphere).
Andromeda is shaped similarly to the Milky Way, but it is larger. As I was staring through my telescope at it, I had the weird thought that perhaps there was some creature on some planet in that galaxy who at that same moment was staring through a telescope at the Milky Way!
I do realize that due to the finite speed of light, I was looking at light that left the Andromeda galaxy a long time ago. Still, I had this image in my mind of me and the Andromedan, each staring at each other through our telescopes!