The coolest part is that because of how light travels, you're actually viewing millions and millions of years in the past.
What mainly interests me, though, is the life that's almost assuredly out there.
It would be unlike anything we have ever seen on this planet, as it would have undergone entirely separate evolution from us.
As crazy as the life we see here is, whatever is out there is orders of magnitude more strange. I mean, this is from Earth:
We can't even imagine the other kinds of life. All movies featuring aliens are creatures that have terrestrial traits, from Greys (which are clearly humanoid/anthropoid in appearance) to squid-like creatures. It shows just how foreign aliens actually will be that we can't imagine anything different to what we already have here.
Fermi Paradox ruins this for me, though.